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A shift-splitting preconditioner for asymmetric saddle point problems
In this paper, we execute the shift-splitting preconditioner for asymmetric
saddle point problems with its (1,2) block's transposition unequal to its (2,1)
block under the removed minus of its (2,1) block. The proposed preconditioner
is stemmed from the shift splitting (SS) iteration method for solving
asymmetric saddle point problems, which is convergent under suitable
conditions. The relaxed version of the shift-splitting preconditioner is
obtained as well. The spectral distributions of the related preconditioned
matrices are given. Numerical experiments from the Stokes problem are offered
to show the convergence performance of these two preconditioners.Comment: 16 pages, 2 figures, Revised on June 10, 202