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Volume 34, Issue 4
A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$

Rong Zhou, Xiang Wang & Peng Zhou

DOI: 10.4208/jcm.1601-m2015-0416

J. Comp. Math., 34 (2016), pp. 437-450.

Published online: 2016-08

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  • Abstract

In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation $AXB = C$ has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficient matrices, although the original coefficient matrices are complex and non-Hermitian. In addition, the optimal parameter of the new iteration method is proposed. Numerical results show that MHSS iteration method is efficient and robust.

  • Keywords

MHSS iteration method, HSS iteration method, Linear matrix equation.

  • AMS Subject Headings

65F10, 65F50.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangxiang49@ncu.edu.cn (Xiang Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-437, author = {Zhou , RongWang , Xiang and Zhou , Peng}, title = {A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {4}, pages = {437--450}, abstract = {

In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation $AXB = C$ has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficient matrices, although the original coefficient matrices are complex and non-Hermitian. In addition, the optimal parameter of the new iteration method is proposed. Numerical results show that MHSS iteration method is efficient and robust.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1601-m2015-0416}, url = {http://global-sci.org/intro/article_detail/jcm/10419.html} }
TY - JOUR T1 - A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$ AU - Zhou , Rong AU - Wang , Xiang AU - Zhou , Peng JO - Journal of Computational Mathematics VL - 4 SP - 437 EP - 450 PY - 2016 DA - 2016/08 SN - 34 DO - http://doi.org/10.4208/jcm.1601-m2015-0416 UR - https://global-sci.org/intro/article_detail/jcm/10419.html KW - MHSS iteration method, HSS iteration method, Linear matrix equation. AB -

In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation $AXB = C$ has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficient matrices, although the original coefficient matrices are complex and non-Hermitian. In addition, the optimal parameter of the new iteration method is proposed. Numerical results show that MHSS iteration method is efficient and robust.

Zhou , RongWang , Xiang and Zhou , Peng. (2016). A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$. Journal of Computational Mathematics. 34 (4). 437-450. doi:10.4208/jcm.1601-m2015-0416
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