{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:33:34Z","timestamp":1776828814299,"version":"3.51.2"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"234","license":[{"start":{"date-parts":[[2001,4,12]],"date-time":"2001-04-12T00:00:00Z","timestamp":987033600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.<\/p>","DOI":"10.1090\/s0025-5718-00-01258-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:17:46Z","timestamp":1027707466000},"page":"649-669","source":"Crossref","is-referenced-by-count":6,"title":["Extreme eigenvalues of real symmetric Toeplitz matrices"],"prefix":"10.1090","volume":"70","author":[{"given":"A.","family":"Melman","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,4,12]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BFb0072474","article-title":"The generalized Schur algorithm for the superfast solution of Toeplitz systems","author":"Ammar, Gregory S.","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/3540172122"},{"key":"2","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/0024-3795(89)90701-5","article-title":"Numerical experience with a superfast real Toeplitz solver","volume":"121","author":"Ammar, Gregory S.","year":"1989","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"key":"3","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/0024-3795(73)90049-9","article-title":"Eigenvectors of certain matrices","volume":"7","author":"Andrew, Alan L.","year":"1973","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1137\/0906025","article-title":"Stability of methods for solving Toeplitz systems of equations","volume":"6","author":"Bunch, James R.","year":"1985","journal-title":"SIAM J. 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