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

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

研究成果: Article

抜粋

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.

元の言語English
ページ(範囲)90-100
ページ数11
ジャーナルElectronics and Communications in Japan (Part III: Fundamental Electronic Science)
74
発行部数11
DOI
出版物ステータスPublished - 1991

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

フィンガープリント Computational complexity of the homotopy method for calculating solutions of strongly monotonic resistive circuit equations' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

  • これを引用