On structured variants of modified HSS iteration methods for complex Toeplitz linear systems. (English) Zbl 1289.65052

Chen, Fang; Jiang, Yaolin; Liu, Qingquan

J. Comput. Math. 31, No. 1, 57-67 (2013).

Summary: The modified Hermitian and skew-Hermitian splitting (MHSS) iteration method was presented and studied by Z. Z. Bai et al. [Computing 87, No. 3–4, 93–111 (2010; Zbl 1210.65074)] for solving a class of complex symmetric linear systems. In this paper, using the properties of the Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear systems. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric Toeplitz linear systems, the computational costs can be considerately reduced by use of Toeplitz structure. Finally, numerical experiments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex Toeplitz linear systems.

MSC:

65F10	Iterative numerical methods for linear systems
65F50	Computational methods for sparse matrices
15B05	Toeplitz, Cauchy, and related matrices
65F08	Preconditioners for iterative methods

Keywords:

Toeplitz matrix; MHSS iteration method; complex symmetric linear system; modified Hermitian and skew-Hermitian splitting iteration method; numerical experiments; preconditioner

Citations:

Zbl 1210.65074