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TitleThe shifted classical circulant and skew circulant splitting iterative methods for Toeplitz matrices
Author(s)Zhongyun Liu
Xiaorong Qin
Nianci Wu
Zhang, Yulin
KeywordsHermitian positive definite
CSCS Splitting
Gauss-Seidel splitting
Toeplitz matrix
Iterative method
Issue date2017
PublisherCanadian Mathematical Society
JournalCanadian 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.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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