Norm bound computation for inverses of linear operators in Hilbert spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Watanabe, Yoshitaka¹  Nagatou, Kaori²  Plum, Michael²  Nakao, Mitsuhiro T.³ 

[1] Kyushu Univ, Res Inst Informat Technol, Higashi Ku, 6-10-1 Hakozaki, Fukuoka 8128518, Japan

[2] Karlsruher Inst Technol, Inst Anal, Englerstr 2, D-76131 Karlsruhe, Germany

[3] Sasebo Coll, Natl Inst Technol, 1-1 Okishin Cho, Sasebo, Nagasaki 8571193, Japan

关键词: Numerical verification;    Solvability of linear problem;    Differential operators;   

DOI  :  10.1016/j.jde.2015.12.041

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free