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A parameterized shift-splitting preconditioner for saddle point problems

Li-Tao Zhang Chao-Qian Li Yao-Tang Li

*Corresponding author: Li-Tao Zhang litaozhang@163.com

MBE2019,2,1021doi:10.3934/mbe.2019048

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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