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.
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