{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:59Z","timestamp":1787336879929,"version":"build-2736575974"},"reference-count":40,"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>Different than for the case of Toeplitz matrix sequences $\\{T_n(f)\\}$, $f\\in L^1$, we can prove that the closure of the union of all the spectra of preconditioned matrix sequences of the form $\\{T_n^{-1}(g)T_n(f)\\}$, $f,g\\in L^1$, $g\\ge 0$, can have gaps if the essential range of f\/g is not connected. The result has important consequences on the practical use of band Toeplitz preconditioners widely used in the literature both for (multilevel) ill-conditioned positive definite and (multilevel) indefinite Toeplitz linear systems.<\/jats:p>","DOI":"10.1137\/s0895479802419269","type":"journal-article","created":{"date-parts":[[2004,4,23]],"date-time":"2004-04-23T21:01:02Z","timestamp":1082754062000},"page":"930-946","source":"Crossref","is-referenced-by-count":0,"title":["The Spectra of Preconditioned Toeplitz Matrix Sequences Can Have Gaps"],"prefix":"10.1137","volume":"25","author":[{"given":"Thomas","family":"Huckle","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Serra-Capizzano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999363188"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)00015-9"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1426-7"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/11.3.333"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595293831"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144594276474"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0910009"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0909051"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(93)90297-9"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575816"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"R. Freund and N. Nachtigal,\n                      A new Krylov\u2010subspace method for symmetric indefinite linear systems\n                      , in Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, W. F. Ames, ed., IMACS, 1994, pp. 1253\u20131256.","DOI":"10.2172\/10190810"},{"key":"R12","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix Computations\n                      , The Johns Hopkins University Press, Baltimore, 1983."},{"key":"R13","unstructured":"U. Grenander and G. Szeg\u00f6,\n                      Toeplitz Forms and Their Applications\n                      , 2nd ed., Chelsea, New York, 1984."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0914034"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502416332"},{"key":"R16","unstructured":"D. Noutsos, S. Serra Capizzano, and P. Vassalos,\n                      A preconditioning proposal for ill\u2010conditioned Hermitian block Toeplitz systems\n                      , Numer. Linear Algebra Appl., to appear."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599351428"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934269"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989427141X"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-97-00833-8"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)80002-5"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)80014-1"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050413"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997329463"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100331"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(01)00361-5"},{"key":"R27","doi-asserted-by":"crossref","unstructured":"Stefano Serra\u2010Capizzano, More inequalities and asymptotics for matrix valued linear positive operators: the noncommutative case, Oper. Theory Adv. Appl., Vol. 135, Birkh\u00e4user, Basel, 2002, 293\u20133152003m:47070","DOI":"10.1007\/978-3-0348-8199-9_18"},{"key":"R28","unstructured":"Stefano Serra Capizzano, Test functions, growth conditions and Toeplitz matrices, Proceedings of the Fourth International Conference on Functional Analysis and Approximation Theory, Vol. II (Potenza, 2000), 2002, 791\u20137952004d:41045"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997329463"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00104-1"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1155\/S1025583402000152"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897331941"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1080\/03081089808818584"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(92)90374-J"},{"key":"R35","doi-asserted-by":"crossref","unstructured":"William Trench, Properties of some generalizations of Kac\u2010Murdock\u2010Szego\u02dd matrices, Contemp. Math., Vol. 281, Amer. Math. Soc., Providence, RI, 2001, 233\u20132452002g:15015","DOI":"10.1090\/conm\/281\/04660"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)00025-5"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)80010-4"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(01)00345-7"},{"key":"R39","volume-title":"Matrix iterative analysis and biorthogonality","author":"Brezinski C.","year":"2002"},{"key":"R40","unstructured":"H. Widom,\n                      Toeplitz matrices\n                      , in Studies in Real and Complex Analysis, I. Hirshman, Jr., ed., Stud. Math. 3, Math. Ass. Amer., Washington, DC, 1965, pp. 179\u2013201."}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479802419269","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:34:51Z","timestamp":1787333691000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479802419269"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0895479802419269"],"URL":"https:\/\/doi.org\/10.1137\/s0895479802419269","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}