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Mathematical Problems in Engineering
Volume 2013, Article ID 438320, 12 pages
http://dx.doi.org/10.1155/2013/438320
Research Article

Real Fast Structure-Preserving Algorithm for Eigenproblem of Complex Hermitian Matrices

1School of Mathematics and Computer Science, Fuzhou University, Fuzhou 351008, China
2School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, China
3School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received 1 January 2013; Accepted 18 February 2013

Academic Editor: Piermarco Cannarsa

Copyright © 2013 Jiangzhou Lai and Linzhang Lu. 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.

Abstract

It is well known that the flops for complex operations are usually 4 times of real cases. In the paper, using real operations instead of complex, a real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices is given. We make use of the real symmetric and skew-Hamiltonian structure transformed by Wilkinson's way, focus on symplectic orthogonal similarity transformations and their structure-preserving property, and then reduce it into a two-by-two block tridiagonal symmetric matrix. Finally a real algorithm can be quickly obtained for eigenvalue problems of the original Hermitian matrix. Numerical experiments show that the fast algorithm can solve real complex Hermitian matrix efficiently, stably, and with high precision.