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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 618380, 9 pages
Research Article

Block Preconditioners for Complex Symmetric Linear System with Two-by-Two Block Form

School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

Received 31 May 2015; Accepted 4 August 2015

Academic Editor: Chih-Cheng Hung

Copyright © 2015 Shi-Liang Wu and Cui-Xia Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on the previous work by Zhang and Zheng (A parameterized splitting iteration method for complex symmetric linear systems, Japan J. Indust. Appl. Math., 31 (2014) 265–278), three block preconditioners for complex symmetric linear system with two-by-two block form are presented. Spectral properties of the preconditioned matrices are discussed in detail. It is shown that all the eigenvalues of the preconditioned matrices are well-clustered. Numerical experiments are reported to illustrate the efficiency of the proposed preconditioners.