A generalization of preconditioned MHSS iteration method for complex symmetric indefinite linear systems

2013 ◽  
Vol 219 (21) ◽  
pp. 10510-10517 ◽  
Author(s):  
Wei-wei Xu
Keyword(s):  
Linear Systems ◽  
Iteration Method ◽  
Complex Symmetric ◽  
Indefinite Linear Systems

On Preconditioned MHSS Real-Valued Iteration Methods for a Class of Complex Symmetric Indefinite Linear Systems

2016 ◽  
Vol 6 (2) ◽  
pp. 192-210 ◽  
Author(s):  
Zhi-Ru Ren ◽  
Yang Cao ◽  
Li-Li Zhang
Keyword(s):  
Linear Systems ◽  
Iteration Method ◽  
Spectral Properties ◽  
Convergence Theory ◽  
Numerical Examples ◽  
Preconditioned Matrix ◽  
Iteration Methods ◽  
Complex Symmetric ◽  
Indefinite Linear Systems

AbstractA generalized preconditioned modified Hermitian and skew-Hermitian splitting (GPMHSS) real-valued iteration method is proposed for a class of complex symmetric indefinite linear systems. Convergence theory is established and the spectral properties of an associated preconditioned matrix are analyzed. We also give several variants of the GPMHSS preconditioner and consider the spectral properties of the preconditioned matrices. Numerical examples illustrate the effectiveness of our proposed method.

Accelerated GPMHSS Method for Solving Complex Systems of Linear Equations

2017 ◽  
Vol 7 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Jing Wang ◽  
Xue-Ping Guo ◽  
Hong-Xiu Zhong
Keyword(s):  
Complex Systems ◽  
Linear Systems ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Splitting Method ◽  
Complex Symmetric Linear Systems ◽  
Systems Of Linear Equations ◽  
Complex Symmetric ◽  
Symmetric Systems

AbstractPreconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

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