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

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 particul...

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Bibliographic Details
Main Authors: Sadeghi, Amir, Md. Ismail, Ahmad Izani
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2012
Subjects:
Online Access:http://eprints.usm.my/38357/
http://eprints.usm.my/38357/1/Approximation_of_the_pth_Roots_of_a_Matrix_by_Using_Trapezoid_Rule.pdf
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Summary: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.