Revista de la
Unión Matemática Argentina
An improved lopsided shift-splitting preconditioner for three-by-three block saddle point problems
Jun Li and Xiangtuan Xiong

Volume 68, no. 1 (2025), pp. 131–144    

Published online (final version): April 3, 2025

https://doi.org/10.33044/revuma.3672

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Abstract

We consider an improved lopsided shift-splitting (ILSS) preconditioner for solving three- by-three block saddle point problems. This method enhances the work of Zhang et al. [Comput. Appl. Math. 41 (2022), 261]. We prove that the iteration method produced by the ILSS preconditioner is unconditionally convergent. Additionally, we show that all eigenvalues of the ILSS preconditioned matrix are real, with non-unit eigenvalues located in a positive interval. Numerical experiments demonstrate the effectiveness of the ILSS preconditioner.

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