### 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 language | English |
---|---|

Pages (from-to) | 90-100 |

Number of pages | 11 |

Journal | Electronics and Communications in Japan (Part III: Fundamental Electronic Science) |

Volume | 74 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1991 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'Computational complexity of the homotopy method for calculating solutions of strongly monotonic resistive circuit equations'. Together they form a unique fingerprint.

## Cite this

*Electronics and Communications in Japan (Part III: Fundamental Electronic Science)*,

*74*(11), 90-100. https://doi.org/10.1002/ecjc.4430741109