Efficient single-step preconditioned HSS iteration methods for complex symmetric linear systems

We propose a single-step preconditioned variant of HSS (SPHSS) and an efficient parameterized SPHSS (PSPHSS) iteration method for solving a class of complex symmetric linear systems. Under suitable conditions, we analyze the convergence properties of the SPHSS and PSPHSS iteration methods. Theoretic...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 74; no. 10; pp. 2269 - 2280
Main Authors Xiao, Xiao-Yong, Wang, Xiang, Yin, Hong-Wei
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 15.11.2017
Elsevier BV
Subjects
Complex symmetric linear system
Convergence analysis
HSS iteration
Iterative methods
Linear equations
Linear systems
Matrices (mathematics)
Numerical analysis
Positive definite
Spectral radius
Studies
Symmetry
Upper bounds
65F50
65F10
Spectral radius
Positive definite
Complex symmetric linear system
HSS iteration
Convergence analysis
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Summary:We propose a single-step preconditioned variant of HSS (SPHSS) and an efficient parameterized SPHSS (PSPHSS) iteration method for solving a class of complex symmetric linear systems. Under suitable conditions, we analyze the convergence properties of the SPHSS and PSPHSS iteration methods. Theoretical analysis shows that the minimal upper bounds for the spectral radius of the SPHSS and PSPHSS iteration matrices are less than those of the SHSS and PSHSS iteration matrices when using the optimal parameters, respectively. Numerical results show that the PSPHSS iteration method has comparable advantage over several other iteration methods whether the experimental optimal parameters are used or not.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.07.007