Norm bound computation for inverses of linear operators in Hilbert spaces

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 estimat...

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Bibliographic Details
Published in:Journal of Differential Equations Vol. 260; no. 7; pp. 6363 - 6374
Main Authors: Watanabe, Yoshitaka, Nagatou, Kaori, Plum, Michael, Nakao, Mitsuhiro T.
Format: Journal Article
Language:English
Published: Elsevier Inc 05.04.2016
Subjects:
Differential operators
Numerical verification
Solvability of linear problem
Solvability of linear problem
Differential operators
65G20
35P15
Numerical verification
47F05
ISSN:0022-0396, 1090-2732
Online Access:Get full text
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2015.12.041