{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:28:00Z","timestamp":1787336880333,"version":"build-2736575974"},"reference-count":22,"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":[[2004,1]]},"abstract":"<jats:p>We propose an algorithm to compute the smallest even and odd eigenvalues of a real symmetric positive-definite Toeplitz matrix, which is based on the factorization of the characteristic polynomial into an even and an odd polynomial. Newton's method is used to compute the smallest even and odd eigenvalues as the smallest roots of the even and odd characteristic polynomials, respectively.<\/jats:p>","DOI":"10.1137\/s0895479803423354","type":"journal-article","created":{"date-parts":[[2004,4,23]],"date-time":"2004-04-23T21:01:02Z","timestamp":1082754062000},"page":"947-963","source":"Crossref","is-referenced-by-count":5,"title":["Computation of the Smallest Even and Odd Eigenvalues of a Symmetric Positive-Definite Toeplitz Matrix"],"prefix":"10.1137","volume":"25","author":[{"given":"A.","family":"Melman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Gregory Ammar, William Gragg, The generalized Schur algorithm for the superfast solution of Toeplitz systems, Lecture Notes in Math., Vol. 1237, Springer, Berlin, 1987, 315\u201333088c:65032","DOI":"10.1007\/BFb0072474"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90707-6"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(73)90049-9"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0906025"},{"key":"R5","first-page":"183","volume":"1","author":"Bunch James","year":"1992","journal-title":"J. Numer. Linear Algebra Appl."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(76)90101-4"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0907009"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"P. Delsarte, Y. Genin, Spectral properties of finite Toeplitz matrices, Lecture Notes in Control and Inform. Sci., Vol. 58, Springer, London, 1984, 194\u201321386k:15003","DOI":"10.1007\/BFb0031053"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1986.1164830"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/1015032"},{"key":"R11","unstructured":"G. Golub and C. Van Loan,\n                      Matrix Computations\n                      , The Johns Hopkins University Press, Baltimore, London, 1996."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/78.175752"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0730078"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895288851"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596314182"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759732229X"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(98)00129-0"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898339621"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-00-01218-7"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(01)00386-X"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1973.tb03424.x"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)10147-7"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479803423354","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:34:52Z","timestamp":1787333692000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479803423354"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0895479803423354"],"URL":"https:\/\/doi.org\/10.1137\/s0895479803423354","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}