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A class of modified DPSS preconditioners for generalized saddle-point linear systems

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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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Acknowledgements

We would like to express our sincere thanks to the two unknown reviewers for their careful reading of the manuscript. Their useful comments and valuable suggestions greatly improve the quality of the paper.

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Correspondence to Zhao-Zheng Liang.

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Communicated by Ernesto G. Birgin.

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This work was supported by the National Natural Science Foundation of China (Nos. 11801242 and 11771193) and the Fundamental Research Funds for the Central Universities (No. lzujbky-2018-31).

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Liang, ZZ., Zhang, GF. A class of modified DPSS preconditioners for generalized saddle-point linear systems. Comp. Appl. Math. 38, 84 (2019). https://doi.org/10.1007/s40314-019-0844-2

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