Norm bound computation for inverses of linear operators in Hilbert spaces

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

    Research output: Contribution to journalArticlepeer-review

    5 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 - Apr 5 2016

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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