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

[摘要] 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.

[学科分类] 数学（综合）

[关键词] saddle point problem;convergence analysis;Krylov subspace iteration methods;preconditioned matrix