Abstract
In this paper, a class of new preconditioners based on matrix splitting are presented for generalized saddle-point linear systems, which improve some recently published preconditioners in view of spectral distributions and numerical performances. Moreover, we widen the scope of the new preconditioners to solve more general but rarely considered saddle-point linear systems with singular leading blocks and rank-deficient off-diagonal blocks. The new variants can result in much better convergence properties and spectrum distributions than the original existing preconditioners. Numerical experiments are given to illustrate the efficiency of the new proposed preconditioners.
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