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Zbl 1185.65055
Gu, Chuanqing; Tian, Zhaolu
On the HSS iteration methods for positive definite Toeplitz linear systems. (English)
[J] J. Comput. Appl. Math. 224, No. 2, 709-718 (2009); erratum ibid. 235, No. 9, 3112-3114 (2011). ISSN 0377-0427

Summary: We study the HSS iteration method for large sparse non-Hermitian positive definite Toeplitz linear systems, which first appears in Bai, Golub and Ng's paper published in 2003 [{\it Z.-Z. Bai, G. H. Golub} and {\it M. K. Ng}, SIAM J. Matrix Anal. Appl. 24, No.~3, 603--626 (2003; Zbl 1036.65032)], and HSS stands for the Hermitian and skew-Hermitian splitting of the coefficient matrix $A$. In this note we use the HSS iteration method based on a special case of the HSS splitting, where the symmetric part $H=\frac 1 2 (A+A^{\text T})$ is a centrosymmetric matrix and the skew-symmetric part $S= \frac {1}{2}(A-A^{\text T})$ is a skew-centrosymmetric matrix for a given Toeplitz matrix. Hence, fast methods are available for computing the two half-steps involved in the HSS and IHSS iteration methods. Some numerical results illustrate their effectiveness.

MSC 2000:: *65F10 Iterative methods for linear systems

Keywords: Toeplitz matrix; centrosymmetric matrix; skew-centrosymmetric matrix; HSS iteration method

Citations: Zbl 1036.65032

Cited in: Zbl 1210.65080

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