@Article{EAJAM-7-530,
author = {},
title = {Efficient Preconditioner and Iterative Method for Large Complex Symmetric Linear Algebraic Systems},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {7},
number = {3},
pages = {530--547},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.240316.290417a},
url = {http://global-sci.org/intro/article_detail/eajam/10763.html}
}