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: Article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English
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Published - 2011
外部発表はい

ASJC Scopus subject areas

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

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