Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Applied numerical linear algebra
Applied numerical linear algebra
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Some properties of centrosymmetric matrices
Applied Mathematics and Computation
Circulant and skew-circulant splitting methods for Toeplitz systems
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
New analogs of split algorithms for arbitrary Toeplitz-plus-Hankelmatrices
IEEE Transactions on Signal Processing
On HSS and AHSS iteration methods for nonsymmetric positive definite Toeplitz systems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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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 [Z.-Z. Bai, G.H. Golub, M.K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl. 24 (2003) 603-626], 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=12(A+A^T) is a centrosymmetric matrix and the skew-symmetric part S=12(A-A^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.