{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:00:26Z","timestamp":1759838426306,"version":"3.40.5"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2022,12,31]]},"DOI":"10.1137\/21m1451440","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T19:48:49Z","timestamp":1669146529000},"page":"1736-1754","source":"Crossref","is-referenced-by-count":2,"title":["Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix"],"prefix":"10.1137","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4779-4800","authenticated-orcid":true,"given":"Siegfried M.","family":"Rump","sequence":"first","affiliation":[{"name":"Institute for Reliable Computing, Hamburg University of Technology, 21073 Hamburg, Germany, and Visiting Professor at Waseda University, Faculty of Science and Engineering, Shinjuku-ku, Tokyo 169\u20138555, Japan ()."}]}],"member":"351","published-online":{"date-parts":[[2022,11,23]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.10.013"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02240207"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/0716028"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-708245-5.50013-0"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02242019"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112511"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/050637601"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01180013"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(93)E0208-4"},{"volume-title":"Lecture Notes for a Summer Course","year":"1968","author":"Kahan W.","key":"ref10"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/050628519"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02235463"},{"volume-title":"MATLAB User\u2019s Guide","year":"1987","key":"ref13"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/140953150"},{"key":"ref15","first-page":"24","volume":"14","author":"Miyajima S.","year":"2010","journal-title":"Reliab. Comput."},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/0714040"},{"volume-title":"Encyclopedia Math. Appl. 37","year":"1990","author":"Neumaier A.","key":"ref17"},{"volume-title":"Principle of Verified Numerical Computations","year":"2018","author":"Oishi S.","key":"ref18"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1247-7_7"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(00)00279-2"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S096249291000005X"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90129-Z"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385508"},{"key":"ref26","first-page":"137","volume":"9","author":"Watanabe Y.","year":"2009","journal-title":"Trans. JSIAM"},{"volume-title":"The Algebraic Eigenvalue Problem","year":"1965","author":"Wilkinson J.","key":"ref27"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396059"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1145\/2576802.2576829"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T16:13:46Z","timestamp":1671725626000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1451440"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,23]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,12,31]]}},"alternative-id":["10.1137\/21M1451440"],"URL":"https:\/\/doi.org\/10.1137\/21m1451440","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"type":"print","value":"0895-4798"},{"type":"electronic","value":"1095-7162"}],"subject":[],"published":{"date-parts":[[2022,11,23]]}}}