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 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.