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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 84-100, 2022/11/23
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.
Keywords: saddle point problem, convergence analysis, Krylov subspace iteration methods, preconditioned matrix