TY - JOUR
T1 - On Structured Variants of Modified HSS Iteration Methods for Complex Toeplitz Linear Systems
AU - Fang Chen, Yaolin Jiang & Qingquan Liu
JO - Journal of Computational Mathematics
VL - 1
SP - 57
EP - 67
PY - 2013
DA - 2013/02
SN - 31
DO - http://doi.org/10.4208/jcm.1208-m4022
UR - https://global-sci.org/intro/article_detail/jcm/9721.html
KW - Toeplitz matrix, MHSS iteration method, Complex symmetric linear system.
AB - <p style="text-align: justify;">The $Modified$ $Hermitian$ $and$ $skew$-$Hermitian$ $splitting$ (MHSS) iteration method was presented and studied by Bai, Benzi and Chen (Computing, 87(2010), 93-111) for solving a class of complex symmetric linear systems. In this paper, using the properties of Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear system. 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 system.</p>