Norm bound computation for inverses of linear operators in Hilbert spaces

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 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 - 2016 Apr 5
Externally publishedYes


  • Differential operators
  • Numerical verification
  • Solvability of linear problem

ASJC Scopus subject areas

  • Analysis


Dive into the research topics of 'Norm bound computation for inverses of linear operators in Hilbert spaces'. Together they form a unique fingerprint.

Cite this