On convergence of splitting iteration methods for non-Hermitian positive-definite linear systems

A new splitting iteration method is presented for the system of linear equations when the coefficient matrix is a non-Hermitian positive-definite matrix. The spectral radius, the optimal parameter, and some norm properties of the iteration matrix for the new method are discussed in detail. Based on...

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Bibliographic Details
Published in:International journal of computer mathematics 2013-02, Vol.90 (2), p.292-305
Main Authors: Wang, Chuan-Long, Yan, Xi-Hong
Format: Article
Language:English
Subjects:
Convergence
iteration method
Iterative methods
Linear equations
Linear systems
Mathematical models
Matrix
non-Hermitian
Norms
Numerical analysis
Optimization
positive-definite matrix
Spectra
Splitting
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Summary:A new splitting iteration method is presented for the system of linear equations when the coefficient matrix is a non-Hermitian positive-definite matrix. The spectral radius, the optimal parameter, and some norm properties of the iteration matrix for the new method are discussed in detail. Based on these results, the new method is convergent under reasonable conditions for any non-Hermitian positive-definite linear system. Finally, the numerical examples show that the new method is more effective than the Hermitian and skew-Hermitian splitting iterative (or positive-definite and skew-Hermitian splitting iterative) method in central processing unit time.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2012.713941