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Abstract and Applied Analysis
Volume 2014, Article ID 978629, 6 pages
Research Article

An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign

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 7 May 2014; Revised 12 July 2014; Accepted 23 July 2014; Published 6 August 2014

Academic Editor: Alicia Cordero

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.


Using the relation between a principal matrix square root and its inverse with the geometric mean, we present a fast algorithm for computing the geometric mean of two Hermitian positive definite matrices. The algorithm is stable and possesses a high convergence order. Some experiments are included to support the proposed computational algorithm.