{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:08:33Z","timestamp":1759838913635},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2006,2,7]],"date-time":"2006-02-07T00:00:00Z","timestamp":1139270400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2006,3]]},"DOI":"10.1007\/s11075-005-9011-5","type":"journal-article","created":{"date-parts":[[2006,2,10]],"date-time":"2006-02-10T14:00:37Z","timestamp":1139580037000},"page":"275-295","source":"Crossref","is-referenced-by-count":5,"title":["Fast computation of two-level circulant preconditioners"],"prefix":"10.1007","volume":"41","author":[{"given":"C.","family":"van der Mee","sequence":"first","affiliation":[]},{"given":"G.","family":"Rodriguez","sequence":"additional","affiliation":[]},{"given":"S.","family":"Seatzu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,2,7]]},"reference":[{"issue":"5","key":"9011_CR1","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/BF01389448","volume":"48","author":"O. Axelsson","year":"1986","unstructured":"O. Axelsson and G. Lindskog, On the rate of convergence of the preconditioned conjugate gradient method, Numer. Math. 48(5) (1986) 499\u2013523.","journal-title":"Numer. Math."},{"key":"9011_CR2","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/79.581363","volume":"14","author":"M.R. Banham","year":"1997","unstructured":"M.R. Banham and A.K. Katsaggelos, Digital image restoration, IEEE Signal Process. Mag. 14 (1997) 24\u201341.","journal-title":"IEEE Signal Process. Mag."},{"key":"9011_CR3","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1137\/0726029","volume":"26","author":"R.H. Chan","year":"1989","unstructured":"R.H. Chan, The spectrum of a family of circulant preconditioned Toeplitz systems, SIAM J. Numer. Anal. 26 (1989) 503\u2013506.","journal-title":"SIAM J. Numer. Anal."},{"key":"9011_CR4","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0024-3795(91)90324-P","volume":"149","author":"R.H. Chan","year":"1991","unstructured":"R.H. Chan, X.Q. Jin and M.C. Yeung, The circulant operator in the Banach algebra of matrices, Linear Algebra Appl. 149 (1991) 41\u201353.","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"9011_CR5","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1137\/0728046","volume":"28","author":"R.H. Chan","year":"1991","unstructured":"R.H. Chan, X.Q. Jin and M.C. Yeung, The spectra of super-optimal circulant preconditioned Toeplitz systems, SIAM J. Numer. Anal. 28(3) (1991) 871\u2013879.","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9011_CR6","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1137\/S0036144594276474","volume":"38","author":"R.H. Chan","year":"1996","unstructured":"R.H. Chan and M.K. Ng, Conjugate gradient methods for Toeplitz systems, SIAM Rev. 38(3) (September 1996) 427\u2013482.","journal-title":"SIAM Rev."},{"issue":"1","key":"9011_CR7","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1137\/0910009","volume":"10","author":"R.H. Chan","year":"1989","unstructured":"R.H. Chan and G. Strang, Toeplitz equations by conjugate gradients with circulant preconditioner, SIAM J. Sci. Statist. Comput. 10(1) (1989) 104\u2013119.","journal-title":"SIAM J. Sci. Statist. Comput."},{"issue":"197","key":"9011_CR8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1090\/S0025-5718-1992-1106960-1","volume":"58","author":"R.H. Chan","year":"1992","unstructured":"R.H. Chan and M.C. Yeung, Circulant preconditioners for Toeplitz matrices with positive continuous generating functions, Math. Comput. 58(197) (1992) 233\u2013240.","journal-title":"Math. Comput."},{"issue":"4","key":"9011_CR9","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1137\/0909051","volume":"9","author":"T.F. Chan","year":"1988","unstructured":"T.F. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. 9(4) (1988) 766\u2013771.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"9011_CR10","volume-title":"Circulant Matrices","author":"P.J. Davis","year":"1979","unstructured":"P.J. Davis, Circulant Matrices, Wiley, New York, 1979."},{"issue":"3","key":"9011_CR11","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1137\/S1064827503421653","volume":"26","author":"F. Benedetto Di","year":"2005","unstructured":"F. Di Benedetto, C. Estatico and S. Serra Capizzano, Superoptimal preconditioned conjugate gradient iteration for image deblurring, SIAM J. Sci. Comput. 26(3) (2005) 1012\u20131035.","journal-title":"SIAM J. Sci. Comput."},{"key":"9011_CR12","doi-asserted-by":"crossref","unstructured":"M. Donatelli, C. Estatico and S. Serra Capizzano, Regularization of image restoration problems with anti-reflective boundary conditions, Submitted, (2004).","DOI":"10.1088\/0266-5611\/21\/1\/011"},{"issue":"4","key":"9011_CR13","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1023\/A:1015222829062","volume":"29","author":"P.C. Hansen","year":"2002","unstructured":"P.C. Hansen, Deconvolution and regularization with Toeplitz matrices, Numer. Algorithms 29(4) (2002) 323\u2013378.","journal-title":"Numer. Algorithms"},{"key":"9011_CR14","first-page":"767","volume":"2","author":"M. Kac","year":"1953","unstructured":"M. Kac, W.L. Murdock and G. Szeg\u00f6, On the eigenvalues of certain Hermitian forms, J. Rat. Mech. Anal. 2 (1953) 767\u2013800.","journal-title":"J. Rat. Mech. Anal."},{"key":"9011_CR15","unstructured":"The MathWorks, Inc., Natick, Massachusetts. Matlab ver. 7.0, 2004."},{"key":"9011_CR16","doi-asserted-by":"crossref","unstructured":"C.V.M. van der Mee, G. Rodriguez and S. Seatzu, Fast superoptimal preconditioning of multiindex Toeplitz matrices. Submitted, (2005).","DOI":"10.1016\/j.laa.2006.02.034"},{"issue":"4","key":"9011_CR17","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1137\/S0895479803432502","volume":"26","author":"C.V.M. Mee van der","year":"2005","unstructured":"C.V.M. van der Mee and S. Seatzu, A method for generating infinite positive self-adjoint test matrices and Riesz bases, SIAM J. Matrix Anal. Appl. 26(4) (2005) 1132\u20131149.","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"9011_CR18","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/S0895479897331941","volume":"21","author":"S. Serra Capizzano","year":"1999","unstructured":"S. Serra Capizzano and E.E. Tyrtyshnikov, Any circulant-like preconditioner for multilevel matrices is not superlinear, SIAM J. Matrix Anal. Appl. 21(2) (1999) 431\u2013439.","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"5","key":"9011_CR19","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/BF01389450","volume":"48","author":"A. Sluis van der","year":"1986","unstructured":"A. van der Sluis and H.A. van der Vorst, The rate of convergence of conjugate gradient. Numer. Math. 48(5) (1986) 543\u2013560.","journal-title":"Numer. Math."},{"key":"9011_CR20","unstructured":"Software in the Public Interest, Inc. Debian\/GNU Linux 3.1 (Sarge), 2005. http:\/\/www.debian.org\/ ."},{"key":"9011_CR21","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1002\/sapm1986742171","volume":"74","author":"G. Strang","year":"1986","unstructured":"G. Strang, A proposal for Toeplitz matrix calculations, Stud. Appl. Math. 74 (1986) 171\u2013176.","journal-title":"Stud. Appl. Math."},{"issue":"213","key":"9011_CR22","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1090\/S0025-5718-96-00682-5","volume":"65","author":"V.V. Strela","year":"1996","unstructured":"V.V. Strela and E.E. Tyrtyshnikov, Which circulant preconditioner is better? Math. Comput. 65(213) (1996) 137\u2013150.","journal-title":"Math. Comput."},{"key":"9011_CR23","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0024-3795(91)90375-7","volume":"154\/156","author":"M. Tismenetsky","year":"1991","unstructured":"M. Tismenetsky, A decomposition of Toeplitz matrices and optimal circulant preconditioning, Linear Algebra Appl. 154\/156 (1991) 105\u2013121.","journal-title":"Linear Algebra Appl."},{"key":"9011_CR24","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1137\/0610010","volume":"10","author":"W.F. Trench","year":"1989","unstructured":"W.F. Trench, Numerical solution of the eigenvalue problem for Hermitian Toeplitz matrices, SIAM J. Matrix Anal. Appl. 10 (1989) 135\u2013146.","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"9011_CR25","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1137\/0613030","volume":"13","author":"E.E. Tyrtyshnikov","year":"1992","unstructured":"E.E. Tyrtyshnikov, Optimal and superoptimal circulant preconditioners, SIAM J. Matrix Anal. Appl. 13(2) (1992) 459\u2013473.","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-005-9011-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-005-9011-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-005-9011-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:06Z","timestamp":1559365686000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-005-9011-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,7]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,3]]}},"alternative-id":["9011"],"URL":"https:\/\/doi.org\/10.1007\/s11075-005-9011-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,2,7]]}}}