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

doi:10.1007/s42967-025-00497-z

Abstract

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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