抄録
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 (English translation of Denshi Tsushin Gakkai Ronbunshi) |
| 巻 | 74 |
| 発行部数 | 11 |
| 出版物ステータス | Published - 1991 11 |
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ASJC Scopus subject areas
- Electrical and Electronic Engineering
これを引用
Computational complexity of the homotopy method for calculating solutions of strongly monotonic resistive circuit equations. / Makino, Mitsunoai; Oishi, Shinichi; Kashiwagi, Masahide; Horiuchi, Kazuo.
：: Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), 巻 74, 番号 11, 11.1991, p. 90-100.研究成果: Article
}
TY - JOUR
T1 - Computational complexity of the homotopy method for calculating solutions of strongly monotonic resistive circuit equations
AU - Makino, Mitsunoai
AU - Oishi, Shinichi
AU - Kashiwagi, Masahide
AU - Horiuchi, Kazuo
PY - 1991/11
Y1 - 1991/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0026259454&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0026259454&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0026259454
VL - 74
SP - 90
EP - 100
JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
SN - 1042-0967
IS - 11
ER -