Class of Uzawa-NPHSS iteration method for solving nonsingular and singular saddle point problems

Based on the non-alternating preconditioned HSS iteration scheme, a class of the Uzawa-NPHSS iteration method for solving nonsingular and singular non-Hermitian saddle point problems with the (1,1) part of the coefficient matrix being non-Hermitian positive definite is established. The convergence p...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 70; no. 14; pp. 2706 - 2738
Main Authors Cheng, Guo, Li, Ji-Cheng
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 22.09.2022
Taylor & Francis Ltd
Subjects
Convergence
Eigenvalues
Eigenvectors
Iterative methods
Matrices (mathematics)
non-alternating preconditioned HSS iteration
Saddle point problem
Saddle points
semi-convergence
Uzawa method
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Summary:Based on the non-alternating preconditioned HSS iteration scheme, a class of the Uzawa-NPHSS iteration method for solving nonsingular and singular non-Hermitian saddle point problems with the (1,1) part of the coefficient matrix being non-Hermitian positive definite is established. The convergence properties for the nonsingular saddle point problems and the semi-convergence properties for the singular ones of the proposed method are carefully discussed under suitable conditions. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analysed in detail. Additionally, the parameter selection strategy for the Uzawa-NPHSS iteration method is provided. Numerical experiments are implemented to confirm the theoretical results, which show the feasibility and effectiveness of the proposed method.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2020.1811628