@article{040c58b0a8554a1e9093604829d029a4,
title = "Some considerations of the invertibility verifications for linear elliptic operators",
abstract = "This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.",
author = "Nakao, {Mitsuhiro T.} and Yoshitaka Watanabe and Takehiko Kinoshita and Takuma Kimura and Nobito Yamamoto",
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. 24340018, 23740074, and 24540151). Publisher Copyright: {\textcopyright} 2015, The JJIAM Publishing Committee and Springer Japan.",
year = "2015",
month = mar,
doi = "10.1007/s13160-014-0160-6",
language = "English",
volume = "32",
pages = "19--31",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "1",
}