A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems

doi:10.1007/s42967-025-00497-z

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 2156-2171.doi: 10.1007/s42967-025-00497-z

• ORIGINAL PAPERS • 上一篇

A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems

Yu-Lan Liu, Bo Wu

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, Ningxia, China

收稿日期:2024-12-11 修回日期:2025-03-24 接受日期:2025-03-27 出版日期:2025-06-18 发布日期:2025-06-18
通讯作者: Bo Wu,E-mail:wubo@nxu.edu.cn E-mail:wubo@nxu.edu.cn
基金资助:
Supported by 2023 autonomous region full-time introduction of high-level talent research project (Grant No. 2023BSB03036) and 2024 higher education science research project of the education department of the autonomous region (NYG2024055).

A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems

Yu-Lan Liu, Bo Wu

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, Ningxia, China

Received:2024-12-11 Revised:2025-03-24 Accepted:2025-03-27 Online:2025-06-18 Published:2025-06-18
Contact: Bo Wu,E-mail:wubo@nxu.edu.cn E-mail:wubo@nxu.edu.cn
Supported by:
Supported by 2023 autonomous region full-time introduction of high-level talent research project (Grant No. 2023BSB03036) and 2024 higher education science research project of the education department of the autonomous region (NYG2024055).

摘要/Abstract

摘要： This paper further extends the shift-splitting (SS) and local shift-splitting (LSS) preconditioners to solve the general block two-by-two linear systems. We demonstrate that the eigenvalues of the corresponding preconditioned matrices cluster tightly around 2 by detailed spectral property analysis. Numerical experiments not only validate the theoretical results but also show the effectiveness and superiority of the SS and LSS preconditioners by comparing them with some existing preconditioners applied to the generalized minimal residual (GMRES) method for solving the block two-by-two linear systems.

关键词: Block two-by-two linear systems, Shift-splitting (SS), Eigenvalues, Preconditioner, Spectral properties

Abstract: This paper further extends the shift-splitting (SS) and local shift-splitting (LSS) preconditioners to solve the general block two-by-two linear systems. We demonstrate that the eigenvalues of the corresponding preconditioned matrices cluster tightly around 2 by detailed spectral property analysis. Numerical experiments not only validate the theoretical results but also show the effectiveness and superiority of the SS and LSS preconditioners by comparing them with some existing preconditioners applied to the generalized minimal residual (GMRES) method for solving the block two-by-two linear systems.

Key words: Block two-by-two linear systems, Shift-splitting (SS), Eigenvalues, Preconditioner, Spectral properties

Yu-Lan Liu, Bo Wu. A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 2156-2171.

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A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems

A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems

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