{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:36:15Z","timestamp":1776800175609,"version":"3.51.2"},"reference-count":9,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T00:00:00Z","timestamp":1467763200000},"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>An important tool to separate zeros of a polynomial according to their moduli without actually computing them is Pellet\u2019s theorem, which unfortunately places severe restrictions on the polynomial\u2019s coefficients. We show that for a class of lacunary polynomials much better results can be obtained by rewriting a polynomial as a matrix polynomial.<\/p>","DOI":"10.1090\/mcom\/3011","type":"journal-article","created":{"date-parts":[[2015,7,6]],"date-time":"2015-07-06T11:39:51Z","timestamp":1436182791000},"page":"707-716","source":"Crossref","is-referenced-by-count":0,"title":["On Pellet\u2019s Theorem for a class of lacunary polynomials"],"prefix":"10.1090","volume":"85","author":[{"given":"A.","family":"Melman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,7,6]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"1708","DOI":"10.1137\/120886741","article-title":"Locating the eigenvalues of matrix polynomials","volume":"34","author":"Bini, Dario A.","year":"2013","journal-title":"SIAM J. Matrix Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4798","issn-type":"print"},{"key":"2","unstructured":"S. Gerschgorin, \u00dcber die Abgrenzung der Eigenwerte einer Matrix. Izv. Akad. Nauk SSSR, Ser. Fiz.-Mat., 6 (1931), 749\u2013754."},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix analysis","author":"Horn, Roger A.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0521305861"},{"key":"4","series-title":"Mathematical Surveys, No. 3","volume-title":"Geometry of polynomials","author":"Marden, Morris","year":"1966","edition":"2"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s11075-013-9705-z","article-title":"Implementation of Pellet\u2019s theorem","volume":"65","author":"Melman, A.","year":"2014","journal-title":"Numer. 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Math., 5 (1881), 393\u2013395."},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1137\/S0036144500381988","article-title":"The quadratic eigenvalue problem","volume":"43","author":"Tisseur, Fran\u00e7oise","year":"2001","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"key":"9","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17798-9","volume-title":"Ger\\v{s}gorin and his circles","volume":"36","author":"Varga, Richard S.","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/3540211004"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-03011-7\/S0025-5718-2015-03011-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-03011-7\/S0025-5718-2015-03011-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:41:59Z","timestamp":1776796919000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-03011-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,6]]},"references-count":9,"journal-issue":{"issue":"298","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["S0025-5718-2015-03011-7"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3011","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":[[2015,7,6]]}}}