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

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

研究成果: ジャーナルへの寄稿記事

抄録

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.

元の言語英語
ページ(範囲)5431-5447
ページ数17
ジャーナルJournal of Differential Equations
266
発行部数9
DOI
出版物ステータス出版済み - 4 15 2019

Fingerprint

Hilbert spaces
Linear Operator
Mathematical operators
Hilbert space
Norm
Alternatives
Numerical Verification
A Priori Error Estimates
Invertibility
Projection

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

これを引用

An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces. / Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.

:: Journal of Differential Equations, 巻 266, 番号 9, 15.04.2019, p. 5431-5447.

研究成果: ジャーナルへの寄稿記事

@article{a4bf7be5835943df9ad7ebd54bca922c,
title = "An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces",
abstract = "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.",
author = "Takehiko Kinoshita and Yoshitaka Watanabe and Nakao, {Mitsuhiro T.}",
year = "2019",
month = "4",
day = "15",
doi = "10.1016/j.jde.2018.10.027",
language = "English",
volume = "266",
pages = "5431--5447",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "9",

}

TY - JOUR

T1 - An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

AU - Kinoshita, Takehiko

AU - Watanabe, Yoshitaka

AU - Nakao, Mitsuhiro T.

PY - 2019/4/15

Y1 - 2019/4/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85055750315&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055750315&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2018.10.027

DO - 10.1016/j.jde.2018.10.027

M3 - Article

AN - SCOPUS:85055750315

VL - 266

SP - 5431

EP - 5447

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 9

ER -