Open AccessA parameterized shift-splitting preconditioner for saddle point problems
Author(s) -
Litao Zhang,
Chaoqian Li,
Yaotang Li
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019048
Subject(s) - preconditioner , saddle point , parameterized complexity , mathematics , intersection (aeronautics) , positive definite matrix , mathematical analysis , linear system , combinatorics , physics , geometry , eigenvalues and eigenvectors , engineering , quantum mechanics , aerospace engineering
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.