Volume 58, pp. 84-100, 2023.

A modified alternating positive semidefinite splitting preconditioner for block three-by-three saddle point problems

Fang Chen and Bi-Cong Ren

Abstract

We propose a modified alternating positive semidefinite splitting (MAPSS) preconditioner for solving block three-by-three saddle point problems that arise in linear programming and the finite element discretization of Maxwell equations. Spectral properties of the MAPSS-preconditioned matrix are discussed and analyzed in detail. As the efficiency of the MAPSS preconditioner depends on its parameters, we derive fast and effective formulas to compute the quasi-optimal values of these parameters. Numerical examples show that the MAPSS preconditioner performs better than the APSS preconditioner.

Full Text (PDF) [908 KB], BibTeX

Key words

saddle point problem, convergence analysis, Krylov subspace iteration methods, preconditioned matrix

AMS subject classifications

65F10, 65F08

Links to the cited ETNA articles

[32]	Vol. 55 (2022), pp. 455-468 Chen Greif: Structured shifts for skew-symmetric matrices

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