An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Kinoshita, Takehiko¹  Watanabe, Yoshitaka²  Nakao, Mitsuhiro T.³ 

[1] 26-1-306 Tanaka Nishiuracho,Sakyo Ku, Kyoto 6068217, Japan

[2] Kyushu Univ, Res Inst Informat Technol, Nishi Ku, 744 Motooka, Fukuoka, Fukuoka 8190395, Japan

[3] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

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

DOI  :  10.1016/j.jde.2018.10.027

来源: Elsevier

【 摘 要 】

In the present paper, we propose a computer-assisted procedure to prove the invertibility of a linear operator in a Hilbert space and to compute a verified norm bound of its inverse. A number of the authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates. The approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications. Several verification examples that confirm the actual effectiveness of the proposed procedure are reported. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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