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Abstract and Applied Analysis
Volume 2015, Article ID 471362, 8 pages
Research Article

Analysis of the Structured Perturbation for the BCSCB Linear System

1Department of Mathematics, Linyi University, Linyi, Shandong 276000, China
2Department of Mathematics, Shandong Normal University, Jinan, Shandong 250014, China

Received 22 July 2014; Accepted 10 September 2014

Academic Editor: Zidong Wang

Copyright © 2015 Xia Tang and Zhaolin Jiang. 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.


Circulant and block circulant type matrices are important tools in solving networked systems. In this paper, based on the style spectral decomposition of the basic circulant matrix and the basic skew circulant matrix, the block style spectral decomposition of the BCSCB matrix is obtained. And then, the structure perturbation is analysed, which includes the condition number and relative error of the BCSCB linear system. Then the optimal backward perturbation bound of the BCSCB linear system is discussed. Simultaneously, the algorithm for the optimal backward perturbation bound is given. Finally, a numerical example is provided to verify the effectiveness of the algorithm.