Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation

Kazuaki Tanaka*, Akitoshi Takayasu, Xuefeng Liu, Shin’ichi Oishi

*この研究の対応する著者

研究成果: Article査読

5 被引用数 (Scopus)

抄録

This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimation is important for verified computations of solutions to elliptic boundary value problems. The proposed method uses a generalized eigenvalue problem to derive the norm estimation. This method has several advantages. Namely, it can be applied to two types of boundary conditions: the Dirichlet type and the Neumann type. It also provides a way of numerically evaluating lower and upper bounds of target eigenvalues. Numerical examples are presented to show that the proposed method provides effective estimations in most cases.

本文言語English
ページ(範囲)665-679
ページ数15
ジャーナルJapan Journal of Industrial and Applied Mathematics
31
3
DOI
出版ステータスPublished - 2014 11 1

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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