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Journal of Applied Mathematics
Volume 2014, Article ID 425654, 9 pages
http://dx.doi.org/10.1155/2014/425654
Research Article

Some Matrix Iterations for Computing Matrix Sign Function

1Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran
2Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 19 December 2013; Revised 29 May 2014; Accepted 2 June 2014; Published 9 July 2014

Academic Editor: Changbum Chun

Copyright © 2014 F. Soleymani et al. 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

Some iterative methods are introduced and demonstrated for finding the matrix sign function. It is analytically shown that the new schemes are asymptotically stable. Convergence analysis along with the error bounds of the main proposed method is established. Different numerical experiments are employed to compare the behavior of the new schemes with the existing matrix iterations of the same type.