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TitleOn circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
Author(s)Liu, Zhongyun
Zhang, Fang
Ferreira, Carla
Zhang, Yulin
KeywordsContinuous Sylvester equations
CSCS iteration
Toeplitz matrices
Issue date2022
JournalComputers and Mathematics With Applications
Abstract(s)We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A and B are Toeplitz matrices. A theoretical study shows that if the circulant and skew-circulant splitting factors of A and B are positive semi-definite (not necessarily Hermitian), and at least one factor is positive definite, then the CSCS method converges to the unique solution of the Sylvester equation. In addition, our analysis gives an upper bound for the convergence factor of the CSCS iteration which depends only on the eigenvalues of the circulant and skew-circulant splitting matrices. A computational comparison with alternative methods reveals the efficiency and reliability of the proposed method.
Publisher version
AccessEmbargoed access (2 Years)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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