ORIGINAL PAPERS

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

  • Yu-Lan Liu ,
  • Bo Wu
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  • School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, Ningxia, China

Received date: 2024-12-11

  Revised date: 2025-03-24

  Accepted date: 2025-03-27

  Online published: 2025-06-18

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).

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.

Cite this article

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 . DOI: 10.1007/s42967-025-00497-z

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