Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 109, Issue -, Pages 30-43Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2022.01.027
Keywords
Continuous Sylvester equations; CSCS iteration; Toeplitz matrices; Convergence
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Funding
- Portuguese Funds through FCT (Fundacao para a Ciencia e a Tecnologia) [UIDB/00013/2020, UIDP/00013/2020]
- NSFC (National Natural Science Foundation of China) [11371075]
- Hunan Key Laboratory of Mathematical Modeling and Analysis in Engineering
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In this article, we propose an iterative method for solving large sparse continuous Sylvester equations. Theoretical analysis shows the convergence and upper bound of the proposed method. Computational comparison with alternative methods demonstrates its efficiency and reliability.
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.
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