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Volume 41, Issue 2
The Variants of the MGSS Methods for Complex Symmetric Linear System of Equations

Changfeng Ma & Xiaojuan Yu

DOI: 10.4208/cmr.2025-0017

Commun. Math. Res., 41 (2025), pp. 173-188.

Published online: 2025-06

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  • Abstract

Recently, inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems, we propose two variants of the modified generalized shift-splitting iteration (MGSS) methods for solving complex symmetric linear systems. One is a parameterized MGSS iteration method and the other is a modified parameterized MGSS iteration method. We prove that the proposed methods are convergent under appropriate constraints on the parameters. In addition, we also give the eigenvalue distributions of different preconditioned matrices to verify the effectiveness of the preconditioners proposed in this paper.

  • Keywords

Complex symmetric linear system, variants of MGSS method, convergence analysis.

  • AMS Subject Headings

15A24, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-41-173, author = {Ma , Changfeng and Yu , Xiaojuan}, title = {The Variants of the MGSS Methods for Complex Symmetric Linear System of Equations}, journal = {Communications in Mathematical Research }, year = {2025}, volume = {41}, number = {2}, pages = {173--188}, abstract = {

Recently, inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems, we propose two variants of the modified generalized shift-splitting iteration (MGSS) methods for solving complex symmetric linear systems. One is a parameterized MGSS iteration method and the other is a modified parameterized MGSS iteration method. We prove that the proposed methods are convergent under appropriate constraints on the parameters. In addition, we also give the eigenvalue distributions of different preconditioned matrices to verify the effectiveness of the preconditioners proposed in this paper.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2025-0017}, url = {http://global-sci.org/intro/article_detail/cmr/24190.html} }
TY - JOUR T1 - The Variants of the MGSS Methods for Complex Symmetric Linear System of Equations AU - Ma , Changfeng AU - Yu , Xiaojuan JO - Communications in Mathematical Research VL - 2 SP - 173 EP - 188 PY - 2025 DA - 2025/06 SN - 41 DO - http://doi.org/10.4208/cmr.2025-0017 UR - https://global-sci.org/intro/article_detail/cmr/24190.html KW - Complex symmetric linear system, variants of MGSS method, convergence analysis. AB -

Recently, inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems, we propose two variants of the modified generalized shift-splitting iteration (MGSS) methods for solving complex symmetric linear systems. One is a parameterized MGSS iteration method and the other is a modified parameterized MGSS iteration method. We prove that the proposed methods are convergent under appropriate constraints on the parameters. In addition, we also give the eigenvalue distributions of different preconditioned matrices to verify the effectiveness of the preconditioners proposed in this paper.

Ma , Changfeng and Yu , Xiaojuan. (2025). The Variants of the MGSS Methods for Complex Symmetric Linear System of Equations. Communications in Mathematical Research . 41 (2). 173-188. doi:10.4208/cmr.2025-0017
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