Norm bound computation for inverses of linear operators in Hilbert spaces

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

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3 Citations (Scopus)


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
Issue number7
Publication statusPublished - Apr 5 2016


All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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