Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/47154

 Title: The shifted classical circulant and skew circulant splitting iterative methods for Toeplitz matrices Author(s): Zhongyun LiuXiaorong QinNianci WuZhang, Yulin Keywords: Hermitian positive definiteCSCS SplittingGauss-Seidel splittingToeplitz matrixIterative method Issue date: 2017 Publisher: Canadian Mathematical Society Journal: Canadian Mathematical Bulletin Abstract(s): It is known that every Toeplitz matrix T enjoys a circulant and skew circulant splitting (denoted by CSCS), i.e., T=C-S with C a circulant matrix and S a skew circulant matrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive definite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss-Seidel (GS) iterative methods if the CSCS is convergent and that there is always a constant $\alpha$ such that the shifted CSCS iteration converges much faster than the Gauss-Seidel iteration, no matter whether the CSCS itself is convergent or not. Type: Article URI: http://hdl.handle.net/1822/47154 DOI: 10.4153/CMB-2016-077-5 ISSN: 0008-4395 e-ISSN: 1496-4287 Publisher version: https://cms.math.ca/10.4153/CMB-2016-077-5 Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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