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

Kiyotaka Yamamura, Kazuo Horiuchi, Shinichi Oishi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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
    Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
    PublisherIEEE
    Pages635-638
    Number of pages4
    Publication statusPublished - 1985

    Fingerprint

    Nonlinear systems
    Numerical analysis
    Decomposition
    Computational efficiency
    Nonlinear equations
    Boundary value problems

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Electronic, Optical and Magnetic Materials

    Cite this

    Yamamura, K., Horiuchi, K., & Oishi, S. (1985). DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS. In Proceedings - IEEE International Symposium on Circuits and Systems (pp. 635-638). IEEE.

    DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS. / Yamamura, Kiyotaka; Horiuchi, Kazuo; Oishi, Shinichi.

    Proceedings - IEEE International Symposium on Circuits and Systems. IEEE, 1985. p. 635-638.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Yamamura, K, Horiuchi, K & Oishi, S 1985, DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS. in Proceedings - IEEE International Symposium on Circuits and Systems. IEEE, pp. 635-638.
    Yamamura K, Horiuchi K, Oishi S. DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS. In Proceedings - IEEE International Symposium on Circuits and Systems. IEEE. 1985. p. 635-638
    Yamamura, Kiyotaka ; Horiuchi, Kazuo ; Oishi, Shinichi. / DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS. Proceedings - IEEE International Symposium on Circuits and Systems. IEEE, 1985. pp. 635-638
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