An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

Abstract

In the present paper, we propose a computer-assisted procedure to prove the invertibility of a linear operator in a Hilbert space and to compute a verified norm bound of its inverse. A number of the authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates. The approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications. Several verification examples that confirm the actual effectiveness of the proposed procedure are reported.

Original languageEnglish
Pages (from-to)5431-5447
Number of pages17
JournalJournal of Differential Equations
Volume266
Issue number9
DOIs
Publication statusPublished - Apr 15 2019

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Hilbert spaces
Linear Operator
Mathematical operators
Hilbert space
Norm
Alternatives
Numerical Verification
A Priori Error Estimates
Invertibility
Projection

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces. / Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.

In: Journal of Differential Equations, Vol. 266, No. 9, 15.04.2019, p. 5431-5447.

Research output: Contribution to journalArticle

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