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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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
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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.
AbstractList	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.
Author	Plum, Michael Nakao, Mitsuhiro T. Nagatou, Kaori Watanabe, Yoshitaka
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Snippet	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...
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SubjectTerms	Differential operators Numerical verification Solvability of linear problem
Title	Norm bound computation for inverses of linear operators in Hilbert spaces
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