An algorithm for finding all solutions of piecewise-linear resistive circuits

Yamamura, Kenichiro; Mishina, M. A.

doi:10.1002/(sici)1097-007x(199603/04)24:2<223::aid-cta889>3.0.co;2-1

Cited by 29 publications

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“…Since the exponential function is monotone and convex, we can use triangles for surrounding the function. [35], [36], [39]- [41]. We applied the LP test algorithm using rectangles, triangles whose two sides are tangents, right-angled triangles, and the improved right-angled triangles.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Finding all solutions of a class of nonlinear equations using an improved LP test

Yamamura

Nakamura

1999

Japan J. Indust. Appl. Math.

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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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Section: Numerical Examplesmentioning

confidence: 99%

“…+ 11.8xiwhich describes a nonlinear resistive circuit containing n tunnel diodes[35]-[39]. We considered the initial region ([-10, 10],..., [-10, 10]) T and applied the LP test algorithms for various n.…”

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confidence: 99%

Finding all solutions of a class of nonlinear equations using an improved LP test

Yamamura

Nakamura

1999

Japan J. Indust. Appl. Math.

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“…For this problem, many efficient algorithms have been developed [1]- [18]. The difficulty of this problem lies in that the number of linear regions is extremely large and the algorithm that searches all the linear regions requires enormous computation time.…”

Section: Introductionmentioning

confidence: 99%

“…The difficulty of this problem lies in that the number of linear regions is extremely large and the algorithm that searches all the linear regions requires enormous computation time. Hence, in the recent algorithms, various techniques are introduced that eliminate many linear regions containing no solution at the same time [8]- [18].…”

Section: Introductionmentioning

confidence: 99%

Finding all solutions of piecewise-linear resistive circuits using linear programming

Yamamura

Ohshima

1998

IEEE Trans. Circuits Syst. I

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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 x x) = 0 (i = 1; 2; 1 1 1 ; 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.Index Terms-Characteristic curves, finding all solutions, linear programming, piecewise-linear resistive circuit.

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“…Over the years, there have been a number of algorithms proposed for finding multiple operating points of circuits [7]- [11]. However, all of these algorithms have the disadvantage of requiring piecewise-linear transistor models; moreover, little insight into the qualitative nature of these multiple operating points is given.…”

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A method for automatically finding multiple operating points in nonlinear circuits

Goldgeisser

Green

2005

IEEE Trans. Circuits Syst. I

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Abstract-A new algorithm based on a SPICE-like simulator that searches for multiple operating points automatically, with no user intervention required, is presented. This algorithm, which exploits the asymmetrical properties of nonlinear mappings that describe multistable circuits, has been implemented into a program which automatically finds multiple (in most cases, all) operating points of a circuit. In addition to finding multiple operating points, this method offers another feature: it is capable of detecting the stability of a particular operating point. Another useful feature of this method is that it allows the user to gauge how close a particular circuit is to possessing multiple operating points. For circuits known to possess multiple operating points, this method allows the user to specify which operating point is encountered first. Unlike other continuation methods, circuit element models are not modified; only augmenting resistors are required. Hence, this approach lends itself well as an "add-on" to existing circuit simulators. A number of circuit examples are given.

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An algorithm for finding all solutions of piecewise-linear resistive circuits

Cited by 29 publications

References 0 publications

Finding all solutions of a class of nonlinear equations using an improved LP test

Finding all solutions of a class of nonlinear equations using an improved LP test

Finding all solutions of piecewise-linear resistive circuits using linear programming

A method for automatically finding multiple operating points in nonlinear circuits

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