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In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.
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참고문헌 (24)
참고문헌 신청
M. Arioli / 1989 / On the augmented system approach to sparse least squares problems / Numer. Math 55(6):667~684
Z.-Z. Bai / 2004 / Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems / Numer. Math 98(1):1~32
Z.-Z. Bai / 2005 / On generalized successive overrelaxation methods for augmented linear systems / Numer. Math 102(1):1~38
A. Berman / 1979 / Nonnegative Matrices in the Mathematical Sciences / Academic Press
Z. Chao / 2014 / Semi-convergence analysis of the Uzawa-SOR methods for singular saddle point problems / Appl. Math. Lett 35:52~57
Z.-Z. Bai / 2004 / Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems / Numer. Math 98(1):1~32
Z.-Z. Bai / 2005 / On generalized successive overrelaxation methods for augmented linear systems / Numer. Math 102(1):1~38
A. Berman / 1979 / Nonnegative Matrices in the Mathematical Sciences / Academic Press
Z. Chao / 2014 / Semi-convergence analysis of the Uzawa-SOR methods for singular saddle point problems / Appl. Math. Lett 35:52~57
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