A fully structured preconditioner for a class of complex symmetric indefinite linear systems

2021 ◽  
Author(s):  
Zhong Zheng ◽  
Jing Chen ◽  
Yue-Fen Chen
Keyword(s):  
Linear Systems ◽  
Complex Symmetric ◽  
Indefinite Linear Systems

An improved block splitting preconditioner for complex symmetric indefinite linear systems

2017 ◽  
Vol 77 (2) ◽  
pp. 451-478 ◽  
Author(s):  
Ju-Li Zhang ◽  
Hong-Tao Fan ◽  
Chuan-Qing Gu
Keyword(s):  
Linear Systems ◽  
Complex Symmetric ◽  
Indefinite Linear Systems

scholarly journals A relaxed block splitting preconditioner for complex symmetric indefinite linear systems

2018 ◽  
Vol 16 (1) ◽  
pp. 561-573
Author(s):  
Yunying Huang ◽  
Guoliang Chen
Keyword(s):  
Linear Systems ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Minimal Polynomial ◽  
Coefficient Matrix ◽  
Subspace Iteration ◽  
Preconditioned Matrix ◽  
Complex Symmetric ◽  
Indefinite Linear Systems

AbstractIn this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the original block two-by-two coefficient matrix. We study the spectral properties and the eigenvector distributions of the corresponding preconditioned matrix. In addition, the degree of the minimal polynomial of the preconditioned matrix is also derived. Finally, some numerical experiments are presented to illustrate the effectiveness of the relaxed splitting preconditioner.

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.

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