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

Abstract EN

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.