@article{b1ad574fc67f4e06a5c0614041a2ff09,
title = "Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces",
abstract = "This paper describes some numerical verification procedures to prove the invertibility of a linear operator in Hilbert spaces and to compute a bound on the norm of its inverse. These approaches improve on previous procedures that use an orthogonal projection of the Hilbert space and its a priori error estimations. Several verified examples which confirm the effectiveness of the new procedures are presented.",
author = "Yoshitaka Watanabe and Takehiko Kinoshita and Nakao, {Mitsuhiro T.}",
note = "Funding Information: The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 21H01000, 21K03373 and 21K03378) and Japan Science and Technology Agency, CREST (No. JPMJCR14D4). The computation was mainly carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University, Japan. Funding Information: The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 21H01000, 21K03373 and 21K03378) and Japan Science and Technology Agency, CREST (No. JPMJCR14D4). The computation was mainly carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University, Japan. Publisher Copyright: {\textcopyright} 2023, The Author(s).",
year = "2023",
month = jan,
doi = "10.1007/s10915-023-02097-6",
language = "English",
volume = "94",
journal = "Journal of Scientific Computing",
issn = "0885-7474",
publisher = "Springer New York",
number = "2",
}