Norm bound computation for inverses of linear operators in Hilbert spaces

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)6363-6374
Number of pages12
JournalJournal of Differential Equations
Volume260
Issue number7
DOIs
Publication statusPublished - 2016 Apr 5
Externally publishedYes

Fingerprint

Invertibility
Hilbert spaces
Enclosures
Partial differential equations
Linear Operator
Mathematical operators
Hilbert space
Norm
A Priori Error Estimates
Enclosure
Bijective
Bounded Operator
Nonlinear Partial Differential Equations
Projection

Keywords

  • Differential operators
  • Numerical verification
  • Solvability of linear problem

ASJC Scopus subject areas

  • Analysis

Cite this

Norm bound computation for inverses of linear operators in Hilbert spaces. / Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.

In: Journal of Differential Equations, Vol. 260, No. 7, 05.04.2016, p. 6363-6374.

Research output: Contribution to journalArticle

Watanabe, Yoshitaka ; Nagatou, Kaori ; Plum, Michael ; Nakao, Mitsuhiro T. / Norm bound computation for inverses of linear operators in Hilbert spaces. In: Journal of Differential Equations. 2016 ; Vol. 260, No. 7. pp. 6363-6374.
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