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

Hong-Yu Wu; Hong-Yu Wu

doi:10.3934/era.2026327

Electronic Research Archive

2026, Volume 34, Issue 10: 7583-7600. doi: 10.3934/era.2026327

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Research article

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

Hong-Yu Wu ^{1,2
,
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1.
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
2.
Hunan Provincial University Key Laboratory for Big Data Analysis and Application, Hunan First Normal University, Changsha 410205, China

Received: 18 April 2026 Revised: 11 August 2026 Accepted: 17 August 2026 Published: 03 September 2026

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.
- block diagonal preconditioner,
- saddle point problem,
- convergence,
- iterative method
Citation: Hong-Yu Wu. A block diagonal preconditioner with two preconditioning matrices for saddle point problems[J]. Electronic Research Archive, 2026, 34(10): 7583-7600. doi: 10.3934/era.2026327

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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.

References

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