TY - JOUR

T1 - Simplicial fixed points algorithms for finding several solutions of nonlinear circuits

AU - Takase, Tadaaki

AU - Oishi, Shin'Ichi

AU - Io, Hideaki

AU - Yamamura, Kiyotaka

PY - 1984

Y1 - 1984

N2 - The fixed‐point algorithm is a method of obtaining the constructive solution of the system of nonlinear equations. the fixed‐point algorithms can roughly be divided into the differential method and the piecewise‐linear method. This paper adopts the fixed‐point algorithm based on piecewise linearization, which does not require considering the differentiability of the system of nonlinear equations, and shows a method for determining more than one solution of the n‐dimensional system of nonlinear equations. the homotopy defined on 0, ∞ × Rn is used. to trace the solution curve of the homotopy, the special decomposition triangulation of 0, ∞ Rn space is required. By providing a new triangulation of 0, ∞ × Rn for Merrill's and Eaves‐Saigal's methods which are typical and based on piecewise linearization, those methods are extended from the methods of obtaining a single solution to the methods of obtaining more than one solution.

AB - The fixed‐point algorithm is a method of obtaining the constructive solution of the system of nonlinear equations. the fixed‐point algorithms can roughly be divided into the differential method and the piecewise‐linear method. This paper adopts the fixed‐point algorithm based on piecewise linearization, which does not require considering the differentiability of the system of nonlinear equations, and shows a method for determining more than one solution of the n‐dimensional system of nonlinear equations. the homotopy defined on 0, ∞ × Rn is used. to trace the solution curve of the homotopy, the special decomposition triangulation of 0, ∞ Rn space is required. By providing a new triangulation of 0, ∞ × Rn for Merrill's and Eaves‐Saigal's methods which are typical and based on piecewise linearization, those methods are extended from the methods of obtaining a single solution to the methods of obtaining more than one solution.

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U2 - 10.1002/ecja.4400670402

DO - 10.1002/ecja.4400670402

M3 - Article

AN - SCOPUS:0021406784

SN - 8756-6621

VL - 67

SP - 1

EP - 10

JO - Electronics and Communications in Japan (Part I: Communications)

JF - Electronics and Communications in Japan (Part I: Communications)

IS - 4

ER -