DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS.

Kiyotaka Yamamura, Kazuo Horiuchi, Shin'ichi Oishi

Research output: Contribution to journalConference article

Abstract

Extensive studies have been carried out on the homotopy continuation algorithms which constructively determine the solution of nonlinear equations. However, their execution speed is greatly decreased when the system of equations becomes large. A decomposition method and acceleration techniques are introduced in order to improve the computational efficiency of the homotopy algorithms. A new algorithm is presented in which the system of equations is decomposed by A. K. Kevorkian's (1981) method, and then a simplicial method, which is a typical homotopy algorithm, is applied. It is shown that this algorithm has local quadratic convergence under some suitable conditions. Application of the algorithm to nonlinear two-point boundary value problems is also discussed and an efficient mesh refinement strategy is given. 10 refs.

Original languageEnglish
Pages (from-to)635-638
Number of pages4
JournalProceedings - IEEE International Symposium on Circuits and Systems
Publication statusPublished - 1985 Dec 1

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ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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