A theorem for numerical verification on local uniqueness of solutions to fixed-point equations

Nobito Yamamoto, Mitsuhiro T. Nakao, Yoshitaka Watanabe

    研究成果: Contribution to journalArticle査読

    3 被引用数 (Scopus)

    抄録

    We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods. We already derived such a theorem in [11], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations.

    本文言語英語
    ページ(範囲)1190-1204
    ページ数15
    ジャーナルNumerical Functional Analysis and Optimization
    32
    11
    DOI
    出版ステータス出版済み - 2011

    All Science Journal Classification (ASJC) codes

    • 分析
    • 信号処理
    • コンピュータ サイエンスの応用
    • 制御と最適化

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