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A parameterized shift-splitting preconditioner for saddle point problems

1 College of Science, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450015, P. R. China
2 College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, P. R. China
3 Henan province Synergy Innovation Center of Aviation economic development, Zhengzhou, Henan, 450015, P. R. China
4 School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan, 650091, P. R. China

Special Issues: Optimization methods in Intelligent Manufacturing

Recently, Chen and Ma [A generalized shift-splitting preconditioner for saddle point problems, Applied Mathematics Letters, 43 (2015) 49-55] introduced a generalized shift-splitting preconditioner for saddle point problems with symmetric positive definite (1,1)-block. In this paper, I establish a parameterized shift-splitting preconditioner for solving the large sparse augmented systems of linear equations. Furthermore, the preconditioner is based on the parameterized shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration, which has the intersection with the generalized shift-splitting preconditioner. In final, one example is provided to confirm the effectiveness.
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Keywords saddle point problem; parameterized shift-splitting; convergence; preconditioner; Eigenvalue

Citation: Li-Tao Zhang, Chao-Qian Li, Yao-Tang Li. A parameterized shift-splitting preconditioner for saddle point problems. Mathematical Biosciences and Engineering, 2019, 16(2): 1021-1033. doi: 10.3934/mbe.2019048

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