Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE, Chengdu, China  

DOI： 10.1109/APCCAS.2018.8605636

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Language：English   Publishing type：Research paper (scientific journal)  

Recently, efficient algorithms have been proposed for finding all solutions of nonlinear equations using linear programming (LP). These algorithms are based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the LP test, a system of nonlinear equations is transformed into an LP problem by surrounding component nonlinear functions by rectangles or right-angled triangles. In this paper, an efficient algorithm is proposed for finding all solutions of weakly nonlinear equations, where component nonlinear functions are surrounded by parallelograms and then the dual simplex method is applied to the LP problem. Numerical examples are given to confirm the effectiveness of the proposed algorithm. © 2006 Wiley Periodicals, Inc.

DOI： 10.1002/ecjc.20220

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SCRIPTA TECHNICA-JOHN WILEY & SONS  

This paper presents an efficient algorithm for finding all characteristic curves of nonlinear resistive circuits. This algorithm is based on interval analysis and a new computational test for nonexistence of a characteristic curve in a given region X. In this test, the simplex method is applied to a linear programming (LP) problem whose feasible region contains all characteristic curves in X. Such an LP problem can be formulated by replacing the component nonlinear functions with auxiliary variables and linear inequalities that are obtained by using interval extensions. If the feasible region of the LP problem is empty (that can be easily checked by the simplex method), then there is no characteristic curve in X. This test is much more powerful than the conventional nonexistence test, which makes the number of analyzed regions much smaller. By numerical examples, it is shown that the proposed algorithm can find all characteristic curves of nonlinear resistive circuits much more efficiently than the conventional algorithm. (C) 2001 Scripta Technica.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SCRIPTA TECHNICA-JOHN WILEY & SONS  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations of the form Pg(x) + Qx - s = 0 in a given region. In the LP test, the system of PWL equations is transformed into an Lf problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, it is shown that the LP test can be performed very efficiently mostly by Phase II of the simplex method. Using the proposed techniques, the number of pivotings in the LP test becomes much smaller, which makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of relatively large scale circuits (including those where the number of variables is 200 and the number of linear regions is 10(200)) in practical computation time. (C) 2001 Scripta Technica.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SCRIPTA TECHNICA-JOHN WILEY & SONS  

This paper proposes an efficient algorithm for finding all solutions of nonlinear resistive circuits. As a computational method of finding all solutions of nonlinear equations, interval analysis is well known, and the Krawczyk algorithm is one of the most typical algorithms of interval analysis. However, the Krawcyzk algorithm is extremely inefficient for circuit equations whose nonlinearity is very great. In this paper, several techniques are proposed for improving the computational efficiency of the Krawczyk algorithm for circuit equations. These techniques exploit the special structure of the circuit equations such as separability Or partial linearity. It is shown that the computation time of the Krawczyk algorithm is substantially decreased by using the proposed techniques. (C) 1997 Scripta Technica, Inc.

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The algorithm of interval analysis proposed by Krawczyk, Moore, and Jones (henceforth called the Krawczyk algorithm) is a well‐known algorithm for finding all solutions of nonlinear equations. In this algorithm, the initial region (which is given by an n‐dimensional rectangle) is divided into small subregions, and the existence of a solution in each subregion is examined. Therefore, it can find all solutions. However, the computation time of the Krawczyk algorithm grows exponentially with the dimension, hence it is not a practical algorithm for large‐scale problems although high‐speed computers are used. In this paper, Kevorkian's method is introduced to the Krawczyk algorithm to improve the computational efficiency. Kevorkian's method is a decomposition method for nonlinear equations. It reduces large‐scale nonlinear equations with sparse Jacobians into smaller equations. By this reduction, the computational efficiency of the Krawczyk algorithm is improved substantially. First, a new algorithm of interval analysis is proposed in which Kevorkian's method is introduced to the Krawczyk algorithm. Then a new permutation algorithm (algorithm for decomposing nonlinear equations) that makes the interval arithmetic well defined is proposed. The effectiveness of the proposed algorithm also is verified by numerical examples. Copyright © 1992 Wiley Periodicals, Inc., A Wiley Company

DOI： 10.1002/ecjc.4430750204

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Language：English   Publishing type：Research paper (scientific journal)  

In nonlinear programming problems, an objective function f(x) is optimized (maximized or minimized) subject to some constraints. Such problems are also called constrained optimization problems. Most of the algorithms in nonlinear programming are classified into two categories: 1) transformation methods
and 2) projection methods. The homotopy methods, which are the subject of this paper, belong to the category of projection methods. The main feature of the homotopy methods compared with other projection methods is that they are good at global convergence (which is lacking in most of the projection methods) but are not good at convergence speed (which is the strong point of most of the projection methods). This paper discusses the homotopy methods in nonlinear programming and show that the piecewise‐linear homotopy method using the Newton homotopy and polyhedral subdivision is very effective for solving nonlinear optimization problems. A new algorithm is proposed that exploits the partial separability and linearity of the Kuhn‐Tucker equations (which appear in the nonlinear programming problems). By this exploitation, the computation efficiency is improved markedly compared with the conventional homotopy methods using simplicial subdivision. Moreover, the proposed algorithm converges quadratically, thus accurate solutions can be obtained rapidly. It is proved also that the proposed algorithm is globally convergent for the constrained convex optimization problems. Except for the shortcoming that the programming is complicated, the proposed algorithm has wellbalanced effectiveness. Copyright © 1991 Wiley Periodicals, Inc., A Wiley Company

DOI： 10.1002/ecjc.4430741004

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For the steady‐state analysis of nonlinear oscillatory circuits, the Newton algorithm proposed by Aprille and Trick is well known. However, often the conventional algorithm needs too many iterations or may not converge, because of the discretization error of numerical integration. This paper discusses in detail the Newton algorithm for the steady‐state analysis, and proposes an efficient algorithm which retains the quadratic convergence in the presence of the error of numerical integration. First, a method of computing the exact Jacobians of the functions obtained by numerical integration is proposed. Then it is shown that the quadratic convergence of the Newton algorithm is retained by suitably controlling the truncation errors of the inner Newton iterations for the corrector equations. The proposed Newton algorithm converges to a solution quadratically even if the step length of the numerical integration is large. Utilizing this property, a mesh refinement strategy is proposed which improves the computational efficiency of the algorithm by determining first an inaccurate solution which is computed by using a large steplength. Then this approximate solution is used for the starting point of the next Newton iteration with a smaller steplength to obtain an accurate numerical solution. Also, it is shown that the foregoing technique can also be applied to the Newton algorithm for computing the bifurcation value of the periodic solutions. The validity and the effectiveness of the proposed method are also verified by numerical examples. Copyright © 1988 Wiley Periodicals, Inc., A Wiley Company

DOI： 10.1002/ecja.4410710602

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Language：Japanese   Publisher：電子情報通信学会  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：University of Louisiana  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

This paper presents efficient and easily implementable methods for the characteristic analysis and tolerance analysis of nonlinear resistive circuits using integer programming. In these methods, the problem of finding all characteristic curves or all solution sets (regions of possible operating points) is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that the proposed methods can easily be implemented without making complicated programs, and that all characteristic curves or all solution sets are obtained by solving mixed integer programming problems several times. Numerical examples are given to confirm the effectiveness of the proposed methods.

DOI： 10.1587/transfun.E99.A.710

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Language：English   Publisher：IEEE  

A simple and efficient method is proposed for finding all characteristic curves of piecevvise-linear resistive circuits using the integer programming solver CPLEX. It is proved that all characteristic curves can be obtained by this method using the manual of CPLEX and the original paper where the algorithm used in CPLEX is proposed. Our method can be implemented easily without writing complex programs, and all characteristic curves are obtained by solving mixed integer programming problems only twice.

DOI： 10.1109/APCCAS.2016.7803939

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Language：English   Publisher：IEEE  

Tracing solution curves of nonlinear equations is an important problem that is widely encountered in science and engineering. As a computational method for tracing solution curves, the predictor-corrector method is well-known. This method is successful when the corrector iteration converges to a point on the same curve as the previous point. However, this method fails when it jumps from one solution curve to another, jumps on a different part of the same curve that has already been traced, or that should be traced much later. In this paper, a simple and practical technique is proposed for reducing the probability that those phenomena occur with a little bit of computational effort.

DOI： 10.1109/APCCAS.2016.7803979

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A simple method is proposed for finding all solutions of piecewise-linear resistive circuits using integer programming. In this method, the problem of finding all solutions is formulated as a mixed integer programming problem, and it is solved by the Microsoft Excel solver, which is included in the most widely distributed and widely used spreadsheet Microsoft Excel. The proposed method can be implemented easily without writing complicated programs, and all solutions (all DC operating points or all characteristic curves) can be obtained using the familiar software Excel.

DOI： 10.1109/APCCAS.2016.7803940

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all DC solutions of nonlinear circuits using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the conventional LP test, a system of nonlinear equations is transformed into a linear programming problem by surrounding component nonlinear functions by rectangles. Then, the emptiness or nonemptiness of the feasible region is checked by the dual simplex method. In this paper, we propose a new LP test algorithm using both rectangles and parallelograms, and shows that the proposed algorithm is more efficient than the conventional algorithms using rectangles only or parallelograms only.

DOI： 10.1109/ECCTD.2015.7300124

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Homotopy methods are known to be effective methods for finding DC operating points of nonlinear circuits with the theoretical guarantee of global convergence. There are several types of homotopy methods; as one of the most efficient methods for solving bipolar transistor circuits, the variable-gain homotopy (VGH) method is well-known. In this paper, we propose an efficient VGH method for solving bipolar and MOS transistor circuits. We also show that the proposed method converges to a stable operating point with high possibility from any initial point. The proposed method is not only globally convergent but also more efficient than the conventional VGH methods. Moreover, it can easily be implemented in SPICE.

DOI： 10.1587/transfun.E97.A.1042

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

A new algorithm is proposed for finding all solutions of piecewise-linear resistive circuits using separable programming. In this algorithm, the problem of finding all solutions is formulated as a separable programming problem, and it is solved by the modified simplex method using the restricted-basis entry rule. Since the modified simplex method finds one solution per application, the proposed algorithm can find all solutions efficiently. Numerical examples are given to confirm the effectiveness of the proposed algorithm.

DOI： 10.1587/transfun.E97.A.1037

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：IEEE  

An efficient and practical method is proposed for finding all characteristic curves of piecewise-linear resistive circuits using integer programming. In this method, the problem of finding all characteristic curves is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that the proposed method can easily be implemented without making complicated programs, and all characteristic curves are obtained by solving mixed integer programming problems only twice. It is also shown that the proposed method can be extended to the tolerance analysis of nonlinear resistive circuits.

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：WILEY-BLACKWELL  

Hybrid equations are often used in the theoretical study of nonlinear resistive circuits because they have an easy-to-analyze structure. They are also advantageous in the numerical analysis of nonlinear resistive circuits because they are separable and consist of a relatively small number of variables. However, the hybrid equations are seldom used in practical applications because their formulation is complicated. In this letter, we propose a simple method for formulating the hybrid equations using SPICE. In the proposed method, we only perform the transient analysis of SPICE on a linear circuit that is obtained through a small modification to the original circuit. It is also shown that state equations for nonlinear dynamic circuits can also be formulated by using the proposed method. Copyright (C) 2011 John Wiley & Sons, Ltd.

DOI： 10.1002/cta.788

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Language：English   Publisher：ELSEVIER SCIENCE BV  

Finding all solutions of nonlinear or piecewise-linear equations is an important problem which is widely encountered in science and engineering. Various algorithms have been proposed for this problem. However, the implementation of these algorithms are generally difficult for non-experts or beginners. In this paper, an efficient method is proposed for finding all solutions of separable systems of piecewise-linear equations using integer programming. In this method, we formulate the problem of finding all solutions by a mixed integer programming problem, and solve it by a high-performance integer programming software such as GLPK, SCIP, or CPLEX. It is shown that the proposed method can be easily implemented without making complicated programs. It is also confirmed by numerical examples that the proposed method can find all solutions of medium-scale systems of piecewise-linear equations in practical computation time. (C) 2012 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cam.2012.01.021

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An efficient and practical method is proposed for finding all solutions of piecewise-linear resistive circuits using integer programming. In this method, we formulate the problem of finding all solutions by a mixed integer programming problem, and solve it by a high-performance integer programming software such as GLPK, SCIP, or CPLEX. It is shown that the proposed method can be easily implemented without making complicated programs. It is also confirmed by numerical examples that the proposed method can find all solutions of medium-scale circuits in practical computation time. © 2011 IEEE.

DOI： 10.1109/ECCTD.2011.6043621

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：ELSEVIER SCIENCE INC  

An efficient algorithm is proposed for finding all solutions of systems of n nonlinear equations. This algorithm is based on interval analysis and a new strategy called LP narrowing. In the LP narrowing strategy, boxes (n-dimensional rectangles in the solution domain) containing no solution are excluded, and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques. Since the LP narrowing is very powerful, all solutions can be found very efficiently. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 5000-50,000 nonlinear equations in practical computation time. (C) 2009 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.amc.2009.05.017

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient and practical algorithm is proposed for finding all DC solutions of nonlinear circuits. This algorithm is based on interval analysis and linear programming techniques. The proposed algorithm is very efficient and can be easily implemented by using the free package GLPK (GNU Linear Programming Kit). By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 2 000 nonlinear circuit equations in practical computation time.

DOI： 10.1587/transfun.E92.A.638

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all DC solutions of nonlinear circuits. This algorithm is based on interval analysis and a new strategy called LP narrowing. In the LP narrowing strategy, boxes (n-dimensional rectangles in the solution domain) containing no solution are excluded, and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques. Since the LP narrowing is very powerful, all solutions can be found very efficiently. By numerical examples, it is shown that the proposed algorithm could find all solutions of large-scale systems of nonlinear circuit equations in practical computation time.

DOI： 10.1109/ISCAS.2009.5118204

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：WILEY-BLACKWELL  

An efficient algorithm is proposed for finding all DC solutions of transistor circuits where characteristics of transistors are represented by piecewise-linear (PWL) convex monotone functions. This algorithm is based on a simple test (termed the linear programming, LP, test) for non-existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem by surrounding, component PWL functions by rectangles. Then the dual simplex method is applied. by which the number of pivotings per region becomes very small. In this letter, we propose a new LP test using the dual simplex method and triangles. The proposed test is not only efficient but also more powerful than the conventional test using the simplex method or rectangles. Copyright (C) 2008 John Wiley & Sons, Ltd.

DOI： 10.1002/cta.472

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Language：English   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

In the tolerance analysis of electronic circuits, the concept of set-valued function is often useful. In this paper, an efficient algorithm is proposed for finding all solution sets of nonlinear resistive circuits described by systems of nonlinear equations containing set-valued functions termed piecewise-trapezoidal (PWT) functions. By numerical examples, the effectiveness of the proposed algorithm is confirmed from various viewpoints. It is also shown that the proposed algorithm could find all solution regions to a system of 1000 PWT equations in practical computation time.

DOI： 10.1142/S021812660800471X

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An efficient algorithm is proposed for finding all solutions of systems of nonlinear equations with separable mappings. This algorithm is based on interval analysis, the dual simplex method, the contraction method, and a special technique which makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 2000 nonlinear equations in acceptable computation time.

DOI： 10.1007/s10543-007-0132-1

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Language：English   Publisher：SPRINGER  

An efficient algorithm is proposed for finding all solutions of systems of nonlinear equations with separable mappings. This algorithm is based on interval analysis, the dual simplex method, the contraction method, and a special technique which makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 2000 nonlinear equations in acceptable computation time.

DOI： 10.1007/s10543-007-0132-1

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

As a powerful computational test for nonexistence of a DC solution of a nonlinear circuit, the LP test is well-known. This test is useful for finding all solutions of nonlinear circuits; it is also useful for verifying the nonexistence of a DC operating point in a given region where operating points should not exist. However, the LP test has not been widely used in practical circuit simulation because the programming is not easy for non-experts or beginners. In this paper, we propose a new LP test that can be easily implemented on SPICE without programming. The proposed test is useful because we can easily check the nonexistence of a solution using SPICE only.

DOI： 10.1093/ietfec/e90-a.8.1661

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

As a powerful computational test for nonexistence of a DC solution of a nonlinear circuit, the LP test is well-known. This test is useful for finding all solutions of nonlinear circuits; it is also useful for verifying the nonexistence of a DC operating point in a given region where operating points should not exist. However, the LP test has not been widely used in practical circuit simulation because the programming is not easy for non-experts or beginners. In this paper, we propose a new LP test that can be easily implemented on SPICE without programming. The proposed test is useful because we can easily check the nonexistence of a solution using SPICE only.

DOI： 10.1093/ietfec/e90-a.8.1661

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Language：English   Publisher：IEEE  

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

Homotopy methods are known to be effective methods for finding dc operating points of nonlinear circuits with the theoretical guarantee of global convergence. There are several types of homotopy methods; as one of the efficient methods for solving bipolar circuits, the variable gain homotopy (VGH) method is well-known. However, in the conventional VGH method, the initial point is sometimes far from the solution because it is given as a solution of a diode circuit. In this brief, we propose an efficient VGH method using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming, although we do not know the homotopy method well. Moreover, since we can use a good initial point, the path following tends to become smooth and efficient.

DOI： 10.1109/TCSII.2007.896935

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Language：English   Publisher：IEEE  

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

As an efficient homotopy method for finding DC operating points of nonlinear circuits, the variable gain homotopy (VGH) method is well-known. However, in the conventional VGH method, the initial point is sometimes far from the solution because it is given as a solution of a diode circuit. In this paper, we propose an efficient VGH method using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming, although we do not know the homotopy method well. Moreover, since we can use a good initial point, the path following tends to become smooth and efficient.

CiNii Books

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Language：English   Publisher：IEEE  

As a powerful computational test for nonexistence of a DC solution of a nonlinear circuit, the LP test is well-known. This test is useful for finding all solutions of nonlinear circuits; it is also useful for verifying the nonexistence of a DC operating point in a given region where operating points should not exist. However, the LP test has not been widely used in practical circuit simulation because the programming is not easy for non-experts or beginners. In this paper, we propose a new LP test that can be easily implemented on SPICE without programming. The proposed test is useful because we can easily check the nonexistence of a solution using SPICE only.

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Language：English   Publisher：IEEE  

An efficient and practical algorithm is proposed for finding all DC solutions of nonlinear circuits. This algorithm is based on interval analysis and linear programming. The proposed algorithm is very efficient and can be easily implemented by using the free package GLPK (GNU Linear Programming Kit). By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 2000 nonlinear circuit equations in practical computation time.

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Language：English   Publisher：IEEE  

In the tolerance analysis of electronic circuits, the concept of set-valued function is often useful. In this paper, an efficient algorithm is proposed for finding all solution sets of nonlinear resistive circuits described by systems of nonlinear equations containing set-valued functions termed piecewise-trapezoidal functions. By numerical examples, the effectiveness of the proposed algorithm is verified from various viewpoints. It is also shown that the proposed algorithm could find all solution regions to a system of 1000 piecewise-trapezoidal equations in practical computation time.

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Language：English   Publisher：IEEE  

In the tolerance analysis of electronic circuits, the concept of set-valued function is often useful. In this paper, an efficient algorithm is proposed for finding all solution sets of nonlinear resistive circuits described by systems of nonlinear equations containing set-valued functions termed piecewise-trapezoidal functions. By numerical examples, the effectiveness of the proposed algorithm is verified from various viewpoints. It is also shown that the proposed algorithm could find all solution regions to a system of 1000 piecewise-trapezoidal equations in practical computation time.

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Language：English   Publisher：IEEE  

Homotopy methods are known to be effective methods for finding DC operating points of nonlinear circuits with the theoretical guarantee of global convergence. There are several types of homotopy methods; as one of the efficient methods for solving bipolar circuits, the variable gain homotopy (VGH) method is well-known. However, in the conventional VGH method, the initial point is sometimes far from the solution because it is given as a solution of a diode circuit. In this paper, we propose an efficient VGH method using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming, although we do not know the homotopy method well. Moreover, since we can use a good initial point, the path following tends to become smooth and efficient.

DOI： 10.1109/MWSCAS.2007.4488677

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques" "easily" "without programming," "although we do not know the homotopy method well."

DOI： 10.1093/ietfec/e89-a.11.3320

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Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

DOI： 10.1093/ietfec/e89-a.11.3306

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

DOI： 10.1093/ietfec/e89-a.11.3306

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Language：English   Publisher：WSEAS Press WSEAS  

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Language：English   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors axe approximated by PWL functions with a very large number of segments. This algorithm is based on the LP test using the dual simplex method, the contraction method, and a special technique that makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 10000(4000).

DOI： 10.1142/S021812660600309X

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Language：English   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors axe approximated by PWL functions with a very large number of segments. This algorithm is based on the LP test using the dual simplex method, the contraction method, and a special technique that makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 10000(4000).

DOI： 10.1142/S021812660600309X

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Language：English   Publisher：IEEE  

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, an improved version of the homotopy method is proposed that can find DC operating points of practical nonlinear circuits smoothly and efficiently. It is also shown that the proposed method can be easily implemented on SPICE without programming.

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Language：English   Publisher：IEEE  

Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques," "easily" "without programming," "although we do not know the homotopy method well."

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Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming. © 2006 IEEE.

DOI： 10.1109/MWSCAS.2006.382046

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Language：English   Publisher：IEEE  

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

DOI： 10.1109/ICCCAS.2006.285157

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Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming. © 2006 IEEE.

DOI： 10.1109/ICCCAS.2006.285157

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Language：English   Publisher：IEEE  

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

DOI： 10.1109/MWSCAS.2006.382046

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Language：English   Publisher：IEEE  

Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques," "easily" "without programming," "although we do not know the homotopy method well."

DOI： 10.1093/ietfec/e89-a.11.3320

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Language：English   Publisher：IEEE  

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

DOI： 10.1093/ietfec/e89-a.11.3306

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, we propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method.

DOI： 10.1093/ietfec/e88-a.10.2554

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Finding DC operating points of transistor circuits is a very important and difficult task. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. For efficiency of homotopy methods, it is important to construct an appropriate homotopy function. In conventional homotopy methods, linear auxiliary functions have been commonly used. In this paper, a homotopy method for solving transistor circuits using a nonlinear auxiliary function is proposed. The proposed method utilizes the nonlinear function closely related to circuit equations to be solved, so that it efficiently finds DC operating points of practical transistor circuits. Numerical examples show that the proposed method is several times more efficient than conventional three homotopy methods.

DOI： 10.1093/ietisy/e88-d.7.1401

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DOI： 10.1093/ietisy/e88-d.7.1401

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms. a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter. an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

DOI： 10.1093/ietfec/e88-a.6.1631

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms. a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter. an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

DOI： 10.1093/ietfec/e88-a.6.1631

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.

DOI： 10.1093/ietfec/e88-a.4.825

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.

DOI： 10.1093/ietfec/e88-a.4.825

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Language：English   Publisher：Institute of Electronics, Information and Communication, Engineers, IEICE  

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, we propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method. Copyright © 2005 The Institute of Electronics, Information and Communication Engineers.

DOI： 10.1093/ietfec/e88-a.10.2554

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Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton- Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, we propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method. © 2005 IEEE.

DOI： 10.1109/ISCAS.2005.1465734

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In this paper, it is shown that various scientific problems such as fixed-point problems, linear programming problems, and nonlinear programming problems can be solved by using the circuit simulator SPICE. The basic idea of the proposed method is that formulas of the homotopy method are described by circuits, and then they are solved by SPICE. Since SPICE is an excellent software that includes various excellent techniques, this approach will make the numerical analysis very efficient, especially for stiff problems. Moreover, for SPICE users, the proposed method will be useful because they can easily solve a broad class of problems by the homotopy method realized on SPICE without programming, although they do not know the homotopy method well. © 2005 IEEE.

DOI： 10.1109/ISCAS.2005.1465448

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Language：English   Publisher：IEEE  

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, we propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method.

DOI： 10.1109/ISCAS.2005.1465734

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Language：English   Publisher：IEEE  

In this paper, it is shown that various scientific problems such as fixed-point problems, linear programming problems, and nonlinear programming problems can be solved by using the circuit simulator SPICE. The basic idea of the proposed method is that formulas of the homotopy method are described by circuits, and then they are solved by SPICE. Since SPICE is an excellent software that includes various excellent techniques, this approach will make the numerical analysis very efficient, especially for stiff problems. Moreover, for SPICE users, the proposed method will be useful because they can easily solve a broad class of problems by the homotopy method realized on SPICE without programming, although they do not know the homotopy method well.

DOI： 10.1109/ISCAS.2005.1465448

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Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton- Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, we propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method. © 2005 IEEE.

DOI： 10.1109/ISCAS.2005.1465734

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Finding DC operating points of transistor circuits is an important and difficult task. The Newton-Raphson method adopted in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. For efficiency of globally convergent homotopy methods, it is important to give an appropriate initial solution as a starting point. However, there are few studies concerning such initial solution algorithms, In this paper, initial solution problems in homotopy methods are discussed, and an effective initial solution algorithm is proposed for globally convergent homotopy methods, which finds DC operating points of transistor circuits efficiently. Numerical examples using practical transistor circuits show the effectiveness of the proposed algorithm.

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (other)  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：WILEY-BLACKWELL  

In this letter, an efficient algorithm is proposed for finding all solutions of non-linear (not piecewise-linear) resistive circuits. This algorithm is based on interval analysis, the dual simplex method, and the contraction methods. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500-700 non-linear circuit equations in acceptable computation time. Copyright (C) 2004 John Wiley Sons, Ltd.

DOI： 10.1002/cta.259

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：WILEY-BLACKWELL  

In this letter, an efficient algorithm is proposed for finding all solutions of non-linear (not piecewise-linear) resistive circuits. This algorithm is based on interval analysis, the dual simplex method, and the contraction methods. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500-700 non-linear circuit equations in acceptable computation time. Copyright (C) 2004 John Wiley Sons, Ltd.

DOI： 10.1002/cta.259

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors are approximated by PWL functions with a very large number of segments. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 10000(4000) for the first time.

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all solutions of nonlinear (not piecewise-linear) resistive circuits with mathematical certainty. This algorith is based on interval analysis, the d al simplex method, and the contraction method. By numerical example, it is shown that the proposed algorith could find all solutions of a system of 2000 nonlinear circuit equations n acceptable computati n time.

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Language：English   Publisher：IEEE  

Finding DC operating points of transistor circuits is it very important and difficult task. The Newton-Raphson method employed in SPICE-like simulators often fails to converge a solution. To overcome this convergence problem. homotopy methods have been studied from various viewpoints. For efficiency of convergent homotopy methods. it is important to construct an appropriate homotopy function. In conventional homotopy methods, linear auxiliary functions have been commonly used. In this paper, a homotopy method using some nolinear auxiliary function is proposed. The proposed method utilizes a non-linear function closly related to circuit equations to be solved, so that it efficiently finds DC operating points of practical transistor circuits. Numerical examples show the effectiveness of the proposed algorithm.

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Language：English   Publisher：IEEE  

Finding DC operating points of transistor circuits is a very important and difficult task. To cope with this difficult task, homotopy methods have been studied from various viewpoints. For efficiency of globally convergent homotopy methods, it is important to construct an appropriate homotopy function. In conventional homotopy methods, linear auxiliary functions have been commonly used. In this paper, a homotopy method using some nonlinear auxiliary function is proposed. The proposed method utilizes a nonlinear function closely related to circuit equations to be solved, so that it efficiently finds DC operating points of practical transistor circuits. Numerical examples show the effectiveness of the proposed algorithm.

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This letter deals with the problem of bounding all solution sets to systems of nonlinear equations where nonlinear terms are described by set-valued functions termed piecewise-trapezoidal functions. Such a problem is important in the numerical computation with guaranteed accuracy and in the analysis of fluctuated systems (such as the tolerance analysis of electronic circuits). It is shown that the proposed algorithm could find all solution sets to a system of 300 piecewise-trapezoidal equations approximately in about 30 hours using a 360 MHz computer.

DOI： 10.1023/A:1024607500624

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DOI： 10.1023/A:1024607500624

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Language：Japanese  

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Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time. © 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0377-0427(02)00731-8

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Language：English   Publisher：ELSEVIER SCIENCE BV  

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time. (C) 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0377-0427(02)00731-8

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits containing bipolar transistors. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution in a given region using linear programming (LP). In the LP test, an LP problem is formulated by surrounding the exponential functions in the Ebers-Moll model by right-angled triangles, and it is solved by LP, for example, by the simplex method. In this paper, it is shown that the LP test can be performed by the dual simplex method, which makes the number of pivotings much smaller. Effectiveness of the proposed technique is confirmed by numerical examples.

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

Recently, an efficient algorithm was proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using the simplex method, which could solve a problem where the number of PWL resistors is 200 and the number of linear regions is 10(200). In this brief, an improved version of this algorithm is proposed, which can be applied to a broader class of PWL resistive circuits and could solve problems where the number of PWL resistors is 500 and the number of linear regions is 10(500) in practical computation time.

DOI： 10.1109/TCSI.2002.807513

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all solutions of nonlinear (not piecewise-linear) resistive circuits with mathematical certainty. This algorithm is based on interval analysis, the dual simplex method, and the contraction method. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500 similar to 700 nonlinear circuit equations in acceptable computation time.

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using the simplex method. By numerical examples, it is shown that the proposed algorithm could find all solutions of relatively large scale problems (including those where the number of PWL resistors is 500 similar to 2 000 and the number of linear regions is 10(500) similar to 1000(2000)) in practical computation time.

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Language：English   Publisher：IEEE  

In this paper, an effective initial solution algorithm is proposed for globally convergent homotopy methods, which Pnds DC operating points of transistor circuits efPciently. A new criterion on the initial solution necessary for guaranteeing the global convergence is presented for a practical class of transistor circuits. Numerical examples show the effectiveness of the proposed algorithm.

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using the simplex method. By numerical examples, it is shown that the proposed algorithm could find all solutions of relatively large scale problems (including those where the number of PWL resistors is 500 similar to 2 000 and the number of linear regions is 10(500) similar to 1000(2000)) in practical computation time.

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Language：English   Publisher：WILEY-BLACKWELL  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non-existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large-scale problems, including those where the number of variables is 300 and the number of linear regions is 10(300), in practical computation time. Copyright (C) 2002 John Wiley Sons, Ltd.

DOI： 10.1002/cta.208

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is proposed for finding all dc solutions of piecewise-linear (PWL) circuits. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region using the dual simplex method. The proposed algorithm also uses a special technique that decreases the number of regions on which the LP test is performed. By numerical examples, it is shown that the proposed algorithm could find all solutions of large scale problems, including those where the number of variables is 500 and the number of linear regions is 10(500), in practical computation time.

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Language：English   Publisher：WILEY-BLACKWELL  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non-existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large-scale problems, including those where the number of variables is 300 and the number of linear regions is 10(300), in practical computation time. Copyright (C) 2002 John Wiley Sons, Ltd.

DOI： 10.1002/cta.208

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Language：English   Publisher：SWETS ZEITLINGER PUBLISHERS  

An efficient algorithm is proposed for finding all solutions of nonlinear equations using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the conventional LP test, the system of nonlinear equations is transformed into an LP problem, to which the simplex method is applied. However, although the LP test is very powerful, it requires many pivotings for each region. In this paper, we use the dual simplex method in the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm can find all solutions of systems of 200 nonlinear equations in practical computation time.

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Finding DC operating-points of nonlinear circuits is an important and difficult task. The Newton-Raphson method employed in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. The fixed-point homotopy method is one of the excellent methods. However, from the viewpoint of implementation, it is important to study it further so that the method can be easily and widely used by many circuit designers. This paper presents a practical method to implement the fixed-point homotopy method. A special circuit called the solution-tracing circuit for the fixed-point homotopy method is proposed. By using this circuit, the solution curves of homotopy equations can be traced by performing the SPICE transient analysis. Therefore, no modification to the existing programs is necessary. Moreover, it is proved that the proposed method is globally convergent. Numerical examples show that the proposed technique is effective and can be easily implemented. By the proposed technique, many SPICE users can easily implement the fixed-point homotopy method.

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Language：English   Publisher：IEEE  

In the tolerance analysis of electronic circuits, the concept of set-valued function is often useful. In this paper, an efficient algorithm is proposed for finding all solution sets of nonlinear resistive circuits described by systems of nonlinear equations containing set-valued functions termed piecewise-trapezoidal functions. By numerical examples, it is shown that the proposed algorithm could find all solution regions to a system of 300 piecewise-trapezoidal equations in practical computation time.

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using inverses of approximate Jacobian matrices. In this letter, an effective technique is proposed for improving the computational efficiency of the algorithm with a little bit of computational effort.

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：JOHN WILEY & SONS LTD  

In this letter, an effective technique is proposed for improving the computational efficiency of the contraction-type LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits. Using the proposed technique, all solutions of a large-scale problem, where the number of variables is 100 and the number of linear regions is 10(100), could be found in less than 10 min using a 360 MHz computer. Copyright (C) 2001 John Wiley & Sons, Ltd.

DOI： 10.1002/cta.159

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：JOHN WILEY & SONS LTD  

In this letter, an effective technique is proposed for improving the computational efficiency of the contraction-type LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits. Using the proposed technique, all solutions of a large-scale problem, where the number of variables is 100 and the number of linear regions is 10(100), could be found in less than 10 min using a 360 MHz computer. Copyright (C) 2001 John Wiley & Sons, Ltd.

DOI： 10.1002/cta.159

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DOI： 10.1002/cta.159

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This paper surveys the research topics and results on nonlinear theory and its applications which have been achieved in Japan or by Japanese researchers during the last decade. The paticular emphasis is placed on chaos, neural networks, nonlinear circuit analysis, nonlinear system theory, and numerical methods for solving nonlinear systems.

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An efficient algorithm is proposed for finding all characteristic curves of nonlinear circuits. This algorithm is based on a simple test for nonexistence of a characteristic curve in a region X. In this test, the dual simplex method is applied to a linear programming problem whose feasible region contains all characteristic curves in X. This test is not only powerful but also efficient and requires only a few pivotings per region. © 2001 IEEE.

DOI： 10.1109/ISCAS.2001.921237

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In this letter, an effective technique is proposed for improving the computational efficiency of the contraction-type LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits. Using the proposed technique, all solutions of a large-scale problem, where the number of variables is 100 and the number of linear regions is 10100, could be found in less than 10 min using a 360 MHz computer.

DOI： 10.1002/cta.159

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. In this algorithm, linear programming problems are formulated by surrounding component nonlinear functions by rectangles. In this letter, it is shown that weakly nonlinear functions ran be surrounded by smaller rectangles, which makes the algorithm very efficient.

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：JOHN WILEY & SONS LTD  

In this letter, the performance of the LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits, is evaluated by numerical experiments. It is shown that the algorithm could find all solutions of large-scale problems (including those where the number of variables is 200-300 and the number of linear regions is 10(200)-10(300)) in practical computation time. Copyright (C) 2000 John Wiley & Sons, Ltd.

DOI： 10.1002/1097-007X(200009/10)28:5<501::AID-CTA116>3.0.CO;2-F

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：JOHN WILEY & SONS LTD  

In this letter, the performance of the LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits, is evaluated by numerical experiments. It is shown that the algorithm could find all solutions of large-scale problems (including those where the number of variables is 200-300 and the number of linear regions is 10(200)-10(300)) in practical computation time. Copyright (C) 2000 John Wiley & Sons, Ltd.

DOI： 10.1002/1097-007X(200009/10)28:5<501::AID-CTA116>3.0.CO;2-F

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP), This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. It is shown that the LP test can deal with nonseparable functions of more than one variable by using more than two-dimensional rectangles. It is also shown that, for bipolar transistor circuits, the LP test becomes more efficient and more powerful by surrounding the exponential functions by right-angled triangles. The proposed algorithm is simple, efficient, and can be easily implemented.

DOI： 10.1109/81.855472

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP), This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. It is shown that the LP test can deal with nonseparable functions of more than one variable by using more than two-dimensional rectangles. It is also shown that, for bipolar transistor circuits, the LP test becomes more efficient and more powerful by surrounding the exponential functions by right-angled triangles. The proposed algorithm is simple, efficient, and can be easily implemented.

DOI： 10.1109/81.855472

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Language：English   Publisher：PHYSICAL SOC JAPAN  

Phase equilibrium behavior was studied for a four-component system which consists of three polystyrene homologs with different molecular weights in methylcyclohexane. By using a refractive index method, a reentrant three-phase equilibrium was observed for the first time. The lower three-phase region appeared near the critical temperature of the binary system of polystyrene with the lowest molecular weight in methylcyclohexane. The characteristics of the observed phase equilibrium behavior was compared with the calculation using a generalized Flory-Huggins theory with an empirically determined interaction parameter.

DOI： 10.1143/JPSJ.69.1741

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Language：English   Publisher：PHYSICAL SOC JAPAN  

Phase equilibrium behavior was studied for a four-component system which consists of three polystyrene homologs with different molecular weights in methylcyclohexane. By using a refractive index method, a reentrant three-phase equilibrium was observed for the first time. The lower three-phase region appeared near the critical temperature of the binary system of polystyrene with the lowest molecular weight in methylcyclohexane. The characteristics of the observed phase equilibrium behavior was compared with the calculation using a generalized Flory-Huggins theory with an empirically determined interaction parameter.

DOI： 10.1143/JPSJ.69.1741

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Language：English   Publisher：スイス、ジュネーブ  

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DOI： 10.1023/A:1009956920204

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Language：English  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed in to an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient.

DOI： 10.1109/ISCAS.2000.858714

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As a computational method to find all solutions of nonlinear equations, interval analysis is well-known. In order to improve the computational efficiency of interval analysis, it is necessary to develop a powerful test for nonexistence of a solution in a given region. In this paper, a new nonexistence test is proposed which is more powerful than the conventional test. The basic idea proposed here is to apply the conventional test to linear combinations of functions. Effective linear combinations are proposed which make the nonexistence test very powerful. Using the proposed techniques, all solutions of nonlinear equations (including a system of 100 nonlinear equations and a system with strong nonlinearity which describes a transistor circuit) could be found very efficiently.

DOI： 10.1023/A:1009956920204

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Language：English   Publisher：IEEE  

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient.

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Language：English   Publisher：KINOKUNIYA CO LTD  

Recently, a new computational test has been proposed for nonexistence of a solution to a system of nonlinear equations using linear programming. This test is termed the LP test. It has been shown that the LP test is much more powerful than the conventional nonexistence test if the system of nonlinear equations consists of many linear terms and a relatively small number of nonlinear terms. By introducing the LP test to interval analysis, all solutions of nonlinear equations can be found very efficiently. In this paper, we propose some techniques for improving the computational efficiency of the LP test in some special cases. Using the proposed techniques, all solutions of a special class of nonlinear equations (including circuit equations) can be found very efficiently.

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Language：English   Publisher：AMER INST PHYSICS  

Tricritical phase equilibrium properties were studied for the ternary solution of two polystyrene homologs in methylcyclohexane by numerical analysis of the generalized Flory-Huggins equation with an empirical interaction parameter and by experimental measurements. For critical solutions at the tricritical molecular weight ratio two-phase coexistence curves were calculated very near to the critical points as 10(-7) in the reduced temperature. The shape of the coexistence curves changed markedly depending on the overall compositions of the solution. For the tricritical solution the coexistence curve was asymmetric due to an interference with the critical line but the asymptotic behavior near the tricritical point was not revealed by the present calculation. Two-phase coexistence curves were measured for ternary solutions with the molecular weight M-1=1.87x10(4) and M-2=41.2x10(4) which yielded the molecular weight ratio 22 close to the empirical tricritical value 23 found in literatures. The coexistence curves measured for solutions not far from the tricritical one exhibited the characteristic features calculated for solutions near the tricritical one. (C) 1999 American Institute of Physics. [S0021-9606(99)51238-5].

DOI： 10.1063/1.479914

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Language：English   Publisher：AMER INST PHYSICS  

Tricritical phase equilibrium properties were studied for the ternary solution of two polystyrene homologs in methylcyclohexane by numerical analysis of the generalized Flory-Huggins equation with an empirical interaction parameter and by experimental measurements. For critical solutions at the tricritical molecular weight ratio two-phase coexistence curves were calculated very near to the critical points as 10(-7) in the reduced temperature. The shape of the coexistence curves changed markedly depending on the overall compositions of the solution. For the tricritical solution the coexistence curve was asymmetric due to an interference with the critical line but the asymptotic behavior near the tricritical point was not revealed by the present calculation. Two-phase coexistence curves were measured for ternary solutions with the molecular weight M-1=1.87x10(4) and M-2=41.2x10(4) which yielded the molecular weight ratio 22 close to the empirical tricritical value 23 found in literatures. The coexistence curves measured for solutions not far from the tricritical one exhibited the characteristic features calculated for solutions near the tricritical one. (C) 1999 American Institute of Physics. [S0021-9606(99)51238-5].

DOI： 10.1063/1.479914

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

Recently, the application of homotopy methods to practical circuit simulation has been remarkably developed, and bipolar analog integrated circuits with more than 10000 elements are now solved efficiently by the homotopy methods, There are several approaches to applying the homotopy methods to large-scale circuit simulation. One of them is combining the publicly available software package of the homotopy methods (such as HOMPACK) with the general-purpose circuit simulators such as SPICE. However, the homotopy method using the fixed-point (FP) homotopy (that is provided as a default in HOMPACK) is not guaranteed to converge for the modified nodal (MN) equations that are used in SPICE. In this paper, we propose a modified algorithm of the homotopy method using the FP homotopy and prove that this algorithm is globally convergent for the MN equations. We also show that the proposed algorithm converges to a stable operating point with high possibility from any initial point.

DOI： 10.1109/81.768822

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (bulletin of university, research institution)  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English  

Recently, the application of homotopy methods to practical circuit simulation has been remarkably developed, and bipolar analog integrated circuits with more than 10 000 elements are now solved efficiently by the homotopy methods. There are several approaches to applying the homotopy methods to largescale circuit simulation. One of them is combining the publicly available software package of the homotopy methods (such as HOMPACK) with the general-purpose circuit simulators such as SPICE. However, the homotopy method using the fixed-point (FP) homotopy (that is provided as a default in HOMPACK) is not guaranteed to converge for the modified nodal (MN) equations that are used in SPICE. In this paper, we propose a modified algorithm of the homotopy method using the FP homotopy and prove that this algorithm is globally convergent for the MN equations. We also show that the proposed algorithm converges to a stable operating point with high possibility from any initial point. © 1999 IEEE.

DOI： 10.1109/81.768822

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Language：English   Publisher：Reseach Society of Nonlinear Theory and Its Applications  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is proposed for finding all solutions of bipolar transistor circuits. This algorithm is based on a simple test that checks the nonexistence of a solution using linear programming. In this lest, right-angled triangles are used for surrounding exponential functions of the Ebers-Moll model, by which the number of inequality constraints decreases and the test becomes efficient and powerful.

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a new test for nonexistence of a solution to a system of piecewise-linear equations f(i)(x) = 0 (i = 1.2.....n) in a super-region. Unlike the conventional sign test, which checks whether the solution surfaces of the single piecewise-linear equations exist or not in a super-region, the new test checks whether they intersect or not in the super-region, Such a test can be performed by using linear programming, It is shown that the simplex method can be performed very efficiently by exploiting the adjacency of super-regions in each step. The proposed algorithm is much more efficient than the conventional sign test algorithms and can find all solutions of large scale circuits very efficiently. Moreover, it can find all characteristic curves of piecewise-linear resistive circuits.

DOI： 10.1109/81.669067

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a new test for nonexistence of a solution to a system of piecewise-linear equations f(i)(x) = 0 (i = 1.2.....n) in a super-region. Unlike the conventional sign test, which checks whether the solution surfaces of the single piecewise-linear equations exist or not in a super-region, the new test checks whether they intersect or not in the super-region, Such a test can be performed by using linear programming, It is shown that the simplex method can be performed very efficiently by exploiting the adjacency of super-regions in each step. The proposed algorithm is much more efficient than the conventional sign test algorithms and can find all solutions of large scale circuits very efficiently. Moreover, it can find all characteristic curves of piecewise-linear resistive circuits.

DOI： 10.1109/81.669067

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Language：English   Publisher：Swets & Zeitlinger Publishers  

DOI： 10.1007/BF02510924

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DOI： 10.1109/81.669067

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：BIT FOUNDATION  

A new computational test is proposed for nonexistence of a solution to a system of nonlinear equations in a convex polyhedral region X. The basic idea proposed here is to formulate a linear programming problem whose feasible region contains all solutions in X. Therefore, if the feasible region is empty (which can be easily checked by Phase I of the simplex method), then the system of nonlinear equations has no solution in X. The linear programming problem is formulated by surrounding the component nonlinear functions by rectangles using interval extensions. This test is much more powerful than the conventional test if the system of nonlinear equations consists of many linear terms and a relatively small number of nonlinear terms. By introducing the proposed test to interval analysis, all solutions of nonlinear equations can be found very efficiently.

DOI： 10.1007/BF02510924

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Language：Japanese   Publisher：電子情報通信学会  

CiNii Books

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Language：English  

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a new test for nonexistence of a solution to a system of piecewise-linear equations fi(x) = 0 (i = 1, 2, ⋯, n) in a superregion. Unlike the conventional sign test, which checks whether the solution surfaces of the single piecewise-linear equations exist or not in a super-region, the new test checks whether they intersect or not in the super-region. Such a test can be performed by using linear programming. It is shown that the simplex method can be performed very efficiently by exploiting the adjacency of super-regions in each step. The proposed algorithm is much more efficient than the conventional sign test algorithms and can find all solutions of large scale circuits very efficiently. Moreover, it can find all characteristic curves of piecewise-linear resistive circuits. © 1998 IEEE.

DOI： 10.1109/81.669067

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Language：English   Publisher：Research Society of Nonlinrar Theory and its Applications  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

In circuit simulation, de operating points of nonlinear circuits are obtained by solving circuit equations. In this paper, we consider ''hybrid equations'' as the circuit equations and discuss the stability of de operating points obtained by solving hybrid equations. We give a simple criterion for identifying unstable operating points from the information of the hybrid equations. We also give a useful criterion for identifying initial points from which homotopy methods converge to stable operating points with high possibility. These results are derived from the theory of de operating point stability developed by M.M. Green and A.N. Willson, Jr.

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Language：English   Publisher：IEEE  

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Language：English   Publisher：I E E E  

A new computational test is proposed for nonexistence of a solution to a system of nonlinear equations in a convex polyhedral region X. The basic idea proposed here is to formulate a linear programming problem whose feasible region contains all solutions in X. Therefore, if the feasible region is empty (which can be easily checked by Phase I of the simplex method), then the system of nonlinear equations has no solution in X. The linear programming problem is formulated by surrounding the component nonlinear functions by rectangles using interval extensions. This test is much more powerful than the conventional test if the system of nonlinear equations consists of many linear terms and a relatively small number of nonlinear terms. By introducing the proposed test to interval analysis, all solutions of nonlinear equations can be found very efficiently.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：Research Society of Nonlinear Theory and its Applications  

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Language：English   Publisher：Research Society of Nonlinear Theory and its Applications  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. The algorithm is based on the idea of ''contraction'' of the solution domain using a sign test. The proposed algorithm is efficient because many large super-regions containing no solution are eliminated in early steps.

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Language：Japanese   Publisher：電子情報通信学会  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (other)   Publisher：電子情報通信学会  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

A simple algorithm is proposed for representing nonseparable functions by equivalent separable functions. In this algorithm, functions are first represented by computational graphs, which are directed graphs representing the computational process of the functions. Then, the vertices of the computational graphs are searched in preorder or postorder, and the transformation to separable forms is performed at the places where it is necessary. By this repetition of the transformation, nonseparable functions are represented by separable functions automatically. The proposed algorithm will be useful in various fields of science and engineering because functions of one variable are easy to deal with.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

A computer algorithm is given for representing functions of many variables by superpositions of functions of one variable and addition, By this algorithm, nonseparable functions are represented in separable forms automatically by computer.

DOI： 10.1109/81.488814

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Language：English   Publisher：John Wiley &amp; Sons Ltd  

An improved version of the sign test algorithm is proposed which is at least several times more efficient than previous algorithms because the average numbers of additions and comparisons in the sign test are reduced to 4n/K and 2n. The proposed algorithm is simple and can be easily programmed using recursive functions. It can also be extended to more general circuits.

DOI： 10.1002/(SICI)1097-007X(199603/04)24:2<223::AID-CTA889>3.0.CO;2-1

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：JOHN WILEY & SONS LTD  

DOI： 10.1002/(SICI)1097-007X(199603/04)24:2<223::AID-CTA889>3.0.CO;2-1

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a new test that checks the nonexistence of solutions to the piecewise-linear equations f_i(x)=0(i=1, 2, ・・・, n) in a super-region. Unlike the conventional sign test, which checks whether the solution surfaces of the single piecewise-linear equations exist or not in a super-region, the new test checks whether the solution surfaces of the single piecewise-linear equations intersect or not in a super-region. Such a test can be performed by using linear programming. It is shown that the simplex method can be performed very efficiently by utilizing the adjacency of super-regions in each step. The proposed algorithm is much more efficient than the conventional sign test algorithms and can find all solutions of large scale circuits very efficiently. Moreover, it can find all characteristic curves of piecewise-linear resistive circuits.

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Language：English  

A computer algorithm is given for representing functions of many variables by superpositions of functions of one variable and addition. By this algorithm, nonseparable functions are represented in separable forms automatically by computer. © 1996 IEEE.

DOI： 10.1109/81.488814

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Language：English   Publisher：Research Society of Nonlinear Theory and its Applications  

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Language：English   Publisher：Research Society of Nonlinear Theory and its Applications  

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Language：English   Publisher：Research Society of Nonlinear Theory and its Applications  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Tracing solution curves of nonlinear equations is an important problem in circuit simulation. In this paper, simple techniques are proposed for improving the computational efficiency of the spherical method, which is a method for tracing solution curves. These techniques are very effective in circuit simulation where solution curves often turn very rapidly. Moreover, they can be easily performed with little computational effort.

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：ECCTD  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is given for finding all solutions of piecewise-linear resistive circuits containing nonseparable transistor models such as the Gummel-Poon model or the Shichman-Hodges model. The proposed algorithm is simple and can be easily programmed using recursive functions.

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits containing sophisticated transistor models such as the Gummel-Poon model or the Shichman-Hodges model. When a circuit contains these nonseparable models, the hybrid equation describing the circuit takes a special structure termed pairwise-separability (or tuplewise-separability). This structure is effectively exploited in the new algorithm. A numerical example is given, and it is shown that all solutions are computed very rapidly.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

A globally and quadratically convergent algorithm is presented for solving nonlinear resistive networks containing transistors modeled by the Gummel-Poon model or the Shichman-Hodges model. This algorithm is based on the Katzenelson algorithm that is globally convergent for a broad class of piecewise-linear resistive networks. An effective restart technique is introduced, by which the algorithm converges to the solutions of the nonlinear resistive networks quadratically. The quadratic convergence is proved and also verified by numerical examples.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is presented for solving nonlinear resistive networks. In this algorithm, the techniques of the piecewise-linear homotopy method are introduced to the Katzenelson algorithm, which is known to be globally convergent for a broad class of piecewise-linear resistive networks. The proposed algorithm has the following advantages over the original Katzenelson algorithm. First, it can be applied directly to nonlinear (not piecewise-linear) network equations. Secondly, it can find the accurate solutions of the nonlinear network equations with quadratic convergence. Therefore, accurate solutions can be computed efficiently without the piecewise-linear modeling process. The proposed algorithm is practically more advantageous than the piecewise-linear homotopy method because it is based on the Katzenelson algorithm that is very popular in circuit simulation and has been implemented on several circuit simulators.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

A simple technique is proposed for improving the convergence of Newton's method in the spherical algorithms, which are methods for tracing solution curves. A numerical example is given in order to show the effectiveness of the proposed technique.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Recently, efficient algorithms that exploit the separability of nonlinear mappings have been proposed for finding all solutions of piecewise-linear resistive circuits. In this letter, it is shown that these algorithms can be extended to circuits containing piecewise-linear resistors that are neither voltage nor current controlled. Using the parametric representation for these resistors, the circuits can be described by systems of nonlinear equations with separable mappings. This separability is effectively exploited in finding all solutions. A numerical example is given, and it is demonstrated that all solutions are computed very rapidly by the new algorithm.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. This makes the number of simultaneous linear equations to be solved much smaller. This test, in its original form, is applied to each linear region; but this is time-consuming because the number of linear regions is generally very large. In this paper, it is shown that the sign test can be applied to super-regions consisting of adjacent linear regions. Therefore, many linear regions are discarded at the same time, and the computational efficiency of the algorithm is substantially improved. The branch-and-bound method is used in applying the sign test to super-regions. Some numerical examples are given, and it is shown that all solutions are computed very rapidly. The proposed algorithm is simple, efficient, and can be easily programmed.

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Finding DC solutions of nonlinear networks is one of the most difficult tasks in circuit simulation, and many circuit designers experience difficulties in finding DC solutions using Newton's method. Piecewise-linear analysis has been studied to overcome this difficulty. However, efficient piecewise-linear algorithms have not been proposed for nonlinear resistive networks containing the Gummel-Poon models or the Shichman-Hodges models. In this paper, a new piecewise-linear algorithm is presented for solving nonlinear resistive networks containing these sophisticated transistor models. The basic idea of the algorithm is to exploit the special structure of the nonlinear network equations, namely, the pairwise-separability. The proposed algorithm is globally convergent and much more efficient than the conventional simplical-type piecewise-linear algorithms.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

Simple techniques are proposed for improving the computational efficiency of spherical algorithms,which are methods for tracing solution curves.These techniques are very effective in practical circuit simulation.Also,the amount of the additional works needed is almost negligible.

CiNii Books

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Language：English   Publisher：Research Society of Nonlinear Theory and its Applications  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. Therefore, the number of simultaneous linear equations to be solved is substantially decreased. This test, in its original form, requires O(Ln2) additions and comparisons in the worst case, where n is the number of variables and L is the number of linear regions. In this paper, an effective technique is proposed that reduces the computational complexity of the sign test to O(Ln). Some numerical examples are given, and it is shown that all solutions can be computed very efficiently. The proposed algorithm is simple and can be easily programmed by using recursive functions.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

This paper presents some simple and practical algorithms for tracing implicitly defined solution curves. These algorithms use hyperspheres instead of hyperplanes that are used in the typical predictor-corrector algorithms. Effective techniques for preventing the ''reversion'' phenomenon of the curve tracing are also proposed. The proposed algorithms are geometrically clear and can be easily programmed.

DOI： 10.1109/81.242328

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Language：English   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

This paper presents an efficient algorithm for finding all solutions of piecewise-linear resistive circuits. The algorithm uses two types of sign tests; one is a new test that is proposed in this paper, and the other is the test proposed by Yamamura and Ochiai. The computational complexity of the new test is much smaller than that of Yamamura and Ochiai's test. These tests eliminate many linear regions that do not contain a solution. Therefore, the number of simultaneous linear equations to be solved is substantially reduced. The proposed algorithm is very simple and much more efficient than Yamamura and Ochiai's algorithm.

DOI： 10.1109/81.242330

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Language：English   Publisher：IEEE  

DOI： 10.1109/81.242330

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Algorithms for computing channel capacity have been proposed by many researchers. Recently, one of the authors proposed an efficient algorithm using Newton's method. Since this algorithm has local quadratic convergence, it is advantageous when we want to obtain a numerical solution with high accuracy. In this letter, it is shown that this algorithm can be extended to the algorithm for computing the constrained capacity, i.e., the capacity of discrete memoryless channels with linear constraints. The global convergence of the extended algorithm is proved, and its effectiveness is verified by numerical examples.

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Language：English  

This paper presents some simple and practical algorithms for tracing implicitly defined solution curves. These algorithms use hyperspheres instead of hyperplanes that are used in the typical predictor—corrector algorithms. Effective techniques for preventing the “reversion” phenomenon of the curve tracing are also proposed. The proposed algorithms are geometrically clear and can be easily programmed. © 1993 IEEE

DOI： 10.1109/81.242328

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

A simple technique is proposed for improving the convergence of Newton′s method in the spherical algorithms,which are methods for tracing solution curves.A numerical example is given in order to show the effectiveness of the proposed technique.

CiNii Books

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

Finding DC solutions of nonlinear networks is one of the most difficult tasks in circuit simulation,and many circuit designers experience difficulties in finding DC solutions using Newton′s met hod.Piecewise-linear analysis has been studied to overcome this difficulty.However,efficient piecewise-linear algorithms have not been proposed for nonlinear resistive networks containing the Gummel-Poon models or the Shichman-Hodges models.In this paper,a new piecewise-linear algorithm is presented for solving nonlinear resistive networks containing these sophisticated transistor models.The basic idea of the algorithm is to exploit the special structure of the nonlinear network equations,namely,the pairwise- separability.The proposed algorithm is globally convergent and much more efficient than the conventional simplicial-type piecewise-linear algorithms.

CiNii Books

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

An efficient algorithm is presented for finding all solutions of piecewise-lineax resistive circuits.In this algorithm,a simple sign test is performed to eliminate many linear regions that do not contain a solution.This makes the number of simultaneous linear equations to be solved much smaller.This test,in its original form,is applied to each linear region;but this is time- consuming because the number of linear regions is generally very large.In this paper,it is shown that the sign test can be applied to super-regions consisting of adjacent linear regions.Therefore, many linear regions are discarded at the same time,and the computational efficiency of the algorithm is substantially improved.The branch-and-bound method is used in applying the sign test to super-regions.Some numerical examples are given,and it is shown that all solutions are computed very rapidly.The proposed algorithm is simple,efficient,and can be easily programmed.

CiNii Books

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Language：English   Publisher：IEEE  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Separability is a valuable property of nonlinear mappings. By exploiting this property, computational complexity of many numerical algorithms can be substantially reduced. In this letter, a new algorithm is presented that detects the separability of nonlinear mappings using the concept of ''computational graph''. A hybrid algorithm using both the top-down search and the bottom-up search is proposed. It is shown that this hybrid algorithm is advantageous in detecting the separability of nonlinear simultaneous functions.

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

This paper presents an efficient algorithm for computing the capacity of discrete memoryless channels. The algorithm uses Newton's method which is known to be quadratically convergent. First, a system of nonlinear equations termed Kuhn-Tucker equations is formulated, which has the capacity as a solution. Then Newton's method is applied to the Kuhn-Tucker equations. Since Newton's method does not guarantee global convergence, a continuation method is also introduced. It is shown that the continuation method works well and the convergence of the Newton algorithm is guaranteed. By numerical examples, effectiveness of the algorithm is verified. Since the proposed algorithm has local quadratic convergence, it is advantageous when we want to obtain a numerical solution with high accuracy.

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

This letter presents an effective technique for the piecewise-linear approximation of nonlinear mappings containing Gummel-Poon models or Shichman-Hodges models. The basic idea is to exploit the pairwise-separability of the nonlinear mappings containing these non-separable models. The proposed piecewise-linear approximation is much more effective than the conventional piecewise-linear approximation using a simplicial subdivision.

DOI： 10.1109/81.168932

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Language：English   Publisher：IEEE  

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Language：English   Publisher：電子情報通信学会  

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

This paper presents an efficient algorithm for finding all solutions of piecewise-linear resistive circuits. First, a technique is proposed that substantially reduces the number of function evaluations needed in the piecewise-linear modeling process. Then a simple and very efficient sign test is proposed that remarkably reduces the number of linear simultaneous equations to be solved for finding all solutions. An effective technique that makes the sign test further more efficient is also introduced. All of the techniques exploit the separability of nonlinear mappings. Some numerical examples are given, and it is shown that all solutions are computed very rapidly. Our algorithm is simple and efficient, and it can be easily programmed.

DOI： 10.1109/81.128015

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Language：English   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

The aim of this article is to show the effectiveness of exploiting separability in numerical analysis of nonlinear systems. Separability is a valuable property of nonlinear mappings which appears with surprising frequency in science and engineering. By exploiting this property, computational complexity of many numerical algorithms can be substantially improved. However, this idea has not been received much attention in the fields of electronics, information and communication engineerings. In recent years, efficient algorithms that exploit the separability have been proposed in the areas of circuit analysis, homotopy methods, integer labeling methods, nonlinear programming, information theory, numerical differentiation, and neural networks. In this article, these algorithms are surveyed, and it is shown that considerable improvement of computational efficiency can be achieved by exploiting the separability.

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Language：English  

This letter presents an effective technique for the piecewise-linear approximation of nonlinear mappings containing Gummel-Poon models or Shichman-Hodges models. The basic idea is to exploit the pairwise-separability of the nonlinear mappings containing these nonseparable models. The proposed piecewise-linear approximation is much more effective than the conventional piecewise-linear approximation using a simplicial subdivision. © 1992 IEEE

DOI： 10.1109/81.168932

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Language：English  

This naner nresents an efficient al2orithm for finding all solutions of piecewise-linear resistive circuits. First, a technique is proposed that substantially reduces the number of function evaluations needed in the piecewise-linear modeling process. Then a simple and very efficient sign test is proposed that remarkably reduces the number of linear simultaneous equations to be solved for finding all solutions. An effective technique that makes the sign test further more efficient is also introduced. All of the techniques exploit the separability of nonlinear mappings. Some numerical examples are given, and it is shown that all solutions are computed very rapidly. Our algorithm is simple and efficient, and it can be easily pro-grammed. © 1992, IEEE. All rights reserved.

DOI： 10.1109/81.128015

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Language：English   Publisher：I E E E  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：IEEE  

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Language：English   Publisher：IEICE-INST ELECTRON INFO COMMUN ENG  

The integer labeling method is a simplicial-type homotopy method for solving systems of nonlinear equations with global convergence. Since this method does not require matrix operations, it is very simple and is suited to parallel computation on array processors. However, the computation time of the integer labeling method grows exponentially with the dimension n, because it uses simplicial subdivision and the number of simplices in an n-dimensional rectangle grows with n!. In this paper, we propose an efficient integer labeling method for solving systems of nonlinear equations with partially-separable mappings. Partially-separable mappings appear in various fields of science and engineering, such as nonlinear programming problems. In our method, the number of function evaluations is largely reduced by making use of the partial separability of nonlinear mappings. That is, function values of separable terms need not be evaluated as long as the labeled simplex is moving within the identical rectangle. Hence, as the the number of separable terms increases, considerable improvement of the computational efficiency can be achieved.

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：The Society of Information Theory and its Applications  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

DOI： 10.1109/43.55173

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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

DOI： 10.1109/43.55173

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：電子情報通信学会  

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Language：Japanese   Publisher：電子情報通信学会  

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Language：English   Publisher：電子情報通信学会  

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