Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices

For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal l...

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Bibliographic Details
Published in:Mathematics of computation 2007-01, Vol.76 (257), p.287-298
Main Authors: Bai, Zhong-Zhi, Golub, Gene H., Li, Chi-Kwong
Format: Article
Language:English
Subjects:
Coefficients
Economic theory
Eigenvalues
Eigenvectors
Exact sciences and technology
Iterative solutions
Linear equations
Linear systems
Mathematics
Matrices
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Perceptron convergence procedure
Sciences and techniques of general use
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Summary:For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned Hermitian and skew-Hermitian splitting iteration methods.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-06-01892-8