On HSS-based constraint preconditioners for generalized saddle-point problems

Authors:
Guo-Feng Zhang;Zhi-Ru Ren;Yuan-Yuan Zhou
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000;Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China 100190;School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000
Venue:
Numerical Algorithms
Year:
2011

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Abstract

For the generalized saddle-point problems with non-Hermitian (1,1) blocks, we present an HSS-based constraint preconditioner, in which the (1,1) block of the preconditioner is constructed by the HSS method for solving the non-Hermitian positive definite linear systems. We analyze the invertibility of the HSS-based constraint preconditioner and prove the convergence of the preconditioned iteration method. Numerical experiments are used to demonstrate the efficiency of the preconditioner as well as the corresponding preconditioned iteration method, especially when the (1,1) block of the saddle-point matrix is essentially non-Hermitian.