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Research Article | Open Access

A block diagonal preconditioner with two preconditioning matrices for saddle point problems

School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
Hunan Provincial University Key Laboratory for Big Data Analysis and Application, Hunan First Normal University, Changsha 410205, China
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Abstract

This paper introduced a block diagonal preconditioner that incorporated two distinct preconditioned matrices for solving saddle point problems. Then we established some convergence conditions for the resulting iterative method under appropriate conditions. Moreover, a spectral property of the preconditioned matrix was also provided. Numerical experiments demonstrated that the proposed preconditioner exhibited superior performance compared with several recently developed preconditioners.

Keywords

block diagonal preconditionersaddle point problemconvergenceiterative method

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Electronic Research Archive
Volume 34 Issue 10,
October 2026
Pages 7583-7600
DOI: 10.3934/era.2026327

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Cite this article:
Wu H-Y. A block diagonal preconditioner with two preconditioning matrices for saddle point problems. Electronic Research Archive, 2026, 34(10): 7583-7600. https://doi.org/10.3934/era.2026327

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Received: 18 April 2026
Revised: 11 August 2026
Accepted: 17 August 2026
Published: 15 October 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)