Norm bound computation for inverses of linear operators in Hilbert spaces

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• 作者：Yoshitaka Watanabe^a ; ^{watanabe@cc.kyushu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Kaori Nagatou^b ; ^{kaori.nagatou@kit.edu" class="auth_mail" title="E-mail the corresponding author} ; Michael Plum^b ; ^{michael.plum@kit.edu" class="auth_mail" title="E-mail the corresponding author} ; Mitsuhiro T. Nakao^c ; ^{mtnakao@sasebo.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65G20 ; 47F05 ; 35P15
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 April 2016
• 年：2016
• 卷：260
• 期：7
• 页码：6363-6374
• 全文大小：386 K

文摘

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.