@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.}",
note = "Funding Information: The authors heartily thank the anonymous referee for their thorough reading and valuable comments. The present study was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15K05012 and 15H03637) and CREST, JST. The computations were carried out primarily using the computer facilities at the Research Institute for Information Technology, Kyushu University, Japan. Funding Information: The authors heartily thank the anonymous referee for their thorough reading and valuable comments. The present study was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15K05012 and 15H03637 ) and CREST, JST . The computations were carried out primarily using the computer facilities at the Research Institute for Information Technology, Kyushu University, Japan. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2019",
month = apr,
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",
}