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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 613840, 8 pages
http://dx.doi.org/10.1155/2014/613840
Research Article

Inversion Free Algorithms for Computing the Principal Square Root of a Matrix

1Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece
2Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou Street, 35100 Lamia, Greece

Received 13 February 2014; Revised 13 May 2014; Accepted 13 May 2014; Published 18 June 2014

Academic Editor: Ram U. Verma

Copyright © 2014 Nicholas Assimakis and Maria Adam. 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

New algorithms are presented about the principal square root of an matrix . In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.