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Abstract and Applied Analysis
Volume 2014, Article ID 105301, 9 pages
Research Article

Approximating the Matrix Sign Function Using a Novel Iterative Method

1Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran
2Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
3Department of Mathematics and Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 19 April 2014; Accepted 6 July 2014; Published 17 July 2014

Academic Editor: Juan R. Torregrosa

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.


This study presents a matrix iterative method for finding the sign of a square complex matrix. It is shown that the sequence of iterates converges to the sign and has asymptotical stability, provided that the initial matrix is appropriately chosen. Some illustrations are presented to support the theory.