{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,26]],"date-time":"2026-10-26T18:27:16Z","timestamp":1793039236437,"version":"4.5.0"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"276","license":[{"start":{"date-parts":[[2012,3,30]],"date-time":"2012-03-30T00:00:00Z","timestamp":1333065600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We present Gerschgorin-type eigenvalue inclusion sets applicable to generalized eigenvalue problems. Our sets are defined by circles in the complex plane in the standard Euclidean metric, and are easier to compute than known similar results. As one application we use our results to provide a forward error analysis for a computed eigenvalue of a diagonalizable pencil.<\/p>","DOI":"10.1090\/s0025-5718-2011-02482-8","type":"journal-article","created":{"date-parts":[[2011,3,30]],"date-time":"2011-03-30T12:27:16Z","timestamp":1301488036000},"page":"2127-2142","source":"Crossref","is-referenced-by-count":14,"title":["Gerschgorin\u2019s theorem for generalized eigenvalue problems in the Euclidean metric"],"prefix":"10.1090","volume":"80","author":[{"given":"Yuji","family":"Nakatsukasa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2011,3,30]]},"reference":[{"key":"1","series-title":"Software, Environments, and Tools","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719581","volume-title":"Templates for the solution of algebraic eigenvalue problems","volume":"11","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0898714710"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00211-007-0082-1","article-title":"On perturbation bounds of generalized eigenvalues for diagonalizable pairs","volume":"107","author":"Chen, Xiao Shan","year":"2007","journal-title":"Numer. 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H.","year":"1965"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02482-8\/S0025-5718-2011-02482-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02482-8\/S0025-5718-2011-02482-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:57:28Z","timestamp":1776790648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02482-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,30]]},"references-count":12,"journal-issue":{"issue":"276","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["S0025-5718-2011-02482-8"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2011-02482-8","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2011,3,30]]}}}