Norm bound computation for inverses of linear operators in Hilbert spaces

Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao

研究成果: Article査読

4 被引用数 (Scopus)

抄録

This paper presents a computer-assisted procedure to prove the invertibility of a linear operator which is the sum of an unbounded bijective and a bounded operator in a Hilbert space, and to compute a bound for the norm of its inverse. By using some projection and constructive a priori error estimates, the invertibility condition together with the norm computation is formulated as an inequality based upon a method originally developed by the authors for obtaining existence and enclosure results for nonlinear partial differential equations. Several examples which confirm the actual effectiveness of the procedure are reported.

本文言語English
ページ(範囲)6363-6374
ページ数12
ジャーナルJournal of Differential Equations
260
7
DOI
出版ステータスPublished - 2016 4 5
外部発表はい

ASJC Scopus subject areas

  • Analysis

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