Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 3 : pp. 530–547
Abstract
We discuss an efficient preconditioner and iterative numerical method to solve large complex linear algebraic systems of the form $(W+iT)u=c$, where $W$ and $T$ are symmetric matrices, and at least one of them is nonsingular. When the real part $W$ is dominantly stronger or weaker than the imaginary part $T$, we propose a block multiplicative (BM) preconditioner or its variant (VBM), respectively. The BM and VBM preconditioned iteration methods are shown to be parameter-free, in terms of eigenvalue distributions of the preconditioned matrix. Furthermore, when the relationship between $W$ and $T$ is obscure, we propose a new preconditioned BM method (PBM) to overcome this difficulty. Both convergent properties of these new iteration methods and spectral properties of the corresponding preconditioned matrices are discussed. The optimal value of iteration parameter for the PBM method is determined. Numerical experiments involving the Helmholtz equation and some other applications show the effectiveness and robustness of the proposed preconditioners and corresponding iterative methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.240316.290417a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 3 : pp. 530–547
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Preconditioner complex linear algebraic systems Krylov subspace method spectral properties convergence.
-
A note on preconditioner for the Ohta–Kawasaki equation
Li, Rui-Xia | Liang, Zhao-Zheng | Zhang, Guo-Feng | Liao, Li-Dan | Zhang, LeiApplied Mathematics Letters, Vol. 85 (2018), Iss. P.132
https://doi.org/10.1016/j.aml.2018.06.006 [Citations: 5] -
Optimizing and improving of the C-to-R method for solving complex symmetric linear systems
Liao, Li-Dan | Zhang, Guo-Feng | Li, Rui-XiaApplied Mathematics Letters, Vol. 82 (2018), Iss. P.79
https://doi.org/10.1016/j.aml.2018.02.020 [Citations: 11] -
On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations
Zeng, Min-Li | Zhang, Guo-FengMathematics, Vol. 8 (2020), Iss. 2 P.208
https://doi.org/10.3390/math8020208 [Citations: 0] -
The generalized C-to-R method for solving complex symmetric indefinite linear systems
Liao, Li-Dan | Zhang, Guo-FengLinear and Multilinear Algebra, Vol. 67 (2019), Iss. 9 P.1727
https://doi.org/10.1080/03081087.2018.1469598 [Citations: 2]