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

Based on the equivalent transformation of the complex coefficient matrix, a fully structured preconditioner which is economic to implement within GMRES acceleration is presented for solving a class of complex symmetric indefinite linear systems. We analyze the computational complexity of the propose...

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Bibliographic Details
Published inBIT Vol. 62; no. 2; pp. 667 - 680
Main Authors Zheng, Zhong, Chen, Jing, Chen, Yue-Fen
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2022
Springer Nature B.V
Subjects
Complexity
Computational Mathematics and Numerical Analysis
Eigenvalues
Linear systems
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Numeric Computing
65F50
Complex symmetric linear system
GMRES method
65F10
Preconditioning
Eigen-properties
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Summary:Based on the equivalent transformation of the complex coefficient matrix, a fully structured preconditioner which is economic to implement within GMRES acceleration is presented for solving a class of complex symmetric indefinite linear systems. We analyze the computational complexity of the proposed preconditioner and show that all eigenvalues of the corresponding preconditioned matrix are clustered at a top half annulus. Compared with some other existing preconditioners, the validity of theoretical analysis and the effectiveness of the proposed preconditioner are verified by numerical experiments.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-021-00887-8