{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:36:03Z","timestamp":1787322963257,"version":"3.56.0"},"reference-count":23,"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":[[1996,10]]},"abstract":"<jats:p>In this paper we present new preconditioning techniques for the solution by the preconditioned conjugate gradient (PCG) method of Hermitian Toeplitz systems with real and non- definite generating functions: actually we extend some results of Chan [IMA J. Numer. Anal., 11 (1991), pp. 333\u2013345] and Di Benedetto, Fiorentino, and Serra [Comput. Math. Appl., 25 (1993), pp. 33\u201345] proved for positive definite Toeplitz systems.<\/jats:p>\n                  <jats:p>Moreover we demonstrate some density properties of the spectra of the preconditioned matrices. Finally, we show that the convergence speed of this PCG method is independent of the dimension of the involved matrices.<\/jats:p>","DOI":"10.1137\/s089547989427141x","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"1007-1019","source":"Crossref","is-referenced-by-count":36,"title":["Preconditioning Strategies for Hermitian Toeplitz Systems with Nondefinite Generating Functions"],"prefix":"10.1137","volume":"17","author":[{"given":"Stefano","family":"Serra","sequence":"first","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\/0609005"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389448"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(83)80009-3"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"D. Bini, F. Di Benedetto,  A new preconditioner for the parallel solution of positive definite Toeplitz systems,  Proc. ACM Symposium on Parallel Algorithms and Architecture, Crete, Greece,  1990,  220\u2013223","DOI":"10.1145\/97444.97688"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0906025"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0610039"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/11.3.333"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0910009"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0909051"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0613032"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0916041"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(93)90297-9"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575816"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594271512"},{"key":"R15","volume-title":"Matrix computations","author":"Golub Gene H.","year":"1983"},{"key":"R16","volume-title":"Toeplitz forms and their applications","author":"Grenander U.","year":"1984"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90107-8"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/0913083"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0614037"},{"key":"R20","unstructured":"B. Musicus,  Levinson and Fast Cholesky Algorithms for Toeplitz and Almost Toeplitz Matrices, Tech. Rep., Research Laboratory of Electronics, MIT, Cambridge, MA,  1981"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934269"},{"key":"R22","unstructured":"S. Serra,  New PCG Based Algorithms for the Solution of Symmetric Toeplitz Systems with  $L^{1}$ Generating Functions, Tech. Report, 10, University of Calabria, Cosenza, Italy,  1995"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970999"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S089547989427141X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:35:53Z","timestamp":1787319353000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S089547989427141X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,10]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,10]]}},"alternative-id":["10.1137\/S089547989427141X"],"URL":"https:\/\/doi.org\/10.1137\/s089547989427141x","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,10]]}}}