A STABLE COUPLED NEWTON'S ITERATION FOR THE MATRIX INVERSE $P$-TH ROOT

Abstract

The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of New-ton's method, but previous researchers have mentioned that some iterations havepoor convergence and stability properties. In this work, a stable recursive techniqueto evaluate an inverse pth root of a given matrix is presented. The scheme is analyzedand its properties are investigated. Computational experiments are also performedto illustrate the strengths and weaknesses of the proposed method.