Computational complexity of the homotopy method for calculating solutions of strongly monotonic resistive circuit equations

Mitsunoai Makino, Shin'ichi Oishi, Masahide Kashiwagi, Kazuo Horiuchi

Research output: Contribution to journalArticle

Abstract

A priori estimation is presented for a computational complexity of the homotopy method applied to a certain class of hybrid equations for nonlinear strongly monotonic resistive circuits. First, an explanation is given as to why a computational complexity of the homotopy method cannot be a priori estimated for calculating solutions of hybrid equations in general. In this paper, the homotopy algorithm is considered in which a numerical path‐following algorithm is executed based on the simplified Newton method. Then by introducing Urabe's theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, it is shown that a computational complexity of the algorithm can be a priori estimated when applied to a certain class of hybrid equations for nonlinear strongly monotonic resistive circuits whose domains are bounded. This paper considers two types of path‐following algorithms: one with a numerical error estimation in the domain of a nonlinear operator; and one with a numerical error estimation in the range of the operator.

Original languageEnglish
Pages (from-to)90-100
Number of pages11
JournalElectronics and Communications in Japan (Part III: Fundamental Electronic Science)
Volume74
Issue number11
DOIs
Publication statusPublished - 1991

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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