On Structured Variants of Modified HSS Iteration Methods for Complex Toeplitz Linear Systems

On Structured Variants of Modified HSS Iteration Methods for Complex Toeplitz Linear Systems

Year:    2013

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 1 : pp. 57–67

Abstract

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1208-m4022

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 1 : pp. 57–67

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Toeplitz matrix MHSS iteration method Complex symmetric linear system.

  1. A class of iteration methods based on the HSS for Toeplitz systems of weakly nonlinear equations

    Zhu, Mu-Zheng | Zhang, Guo-Feng

    Journal of Computational and Applied Mathematics, Vol. 290 (2015), Iss. P.433

    https://doi.org/10.1016/j.cam.2015.05.027 [Citations: 9]
  2. Onk-step CSCS-based polynomial preconditioners for Toeplitz linear systems with application to fractional diffusion equations

    Gu, Xian-Ming | Huang, Ting-Zhu | Li, Hou-Biao | Li, Liang | Luo, Wei-Hua

    Applied Mathematics Letters, Vol. 42 (2015), Iss. P.53

    https://doi.org/10.1016/j.aml.2014.11.005 [Citations: 21]
  3. Structured least-squares problems and inverse eigenvalue problems for -reflexive matrices

    Zhao, Meixiang | Jia, Zhigang

    Applied Mathematics and Computation, Vol. 235 (2014), Iss. P.87

    https://doi.org/10.1016/j.amc.2014.02.098 [Citations: 1]