International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 634698, 13 pages
Research Article

Approximation of the pth Roots of a Matrix by Using Trapezoid Rule

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 23 August 2011; Accepted 18 October 2011

Academic Editor: Qing-Wen Wang

Copyright © 2012 Amir Sadeghi and Ahmad Izani Md. Ismail. 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.


The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the trapezoid rule. In this paper, we aim to give a brief overview of the computation of roots of positive definite matrices by employing integral representation. Some numerical experiments are given to illustrate the theoretical results.