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

Abstract

<span>The computation of the inverse roots of matrices arises in evaluating non-symmetric</span><br /><span>eigenvalue problems, solving nonlinear matrix equations, computing some matrix</span><br /><span>functions, control theory and several other areas of applications. It is possible to</span><br /><span>approximate the matrix inverse pth roots by exploiting a specialized version of New-</span><br /><span>ton's method, but previous researchers have mentioned that some iterations have</span><br /><span>poor convergence and stability properties. In this work, a stable recursive technique</span><br /><span>to evaluate an inverse pth root of a given matrix is presented. The scheme is analyzed</span><br /><span>and its properties are investigated. Computational experiments are also performed</span><br /><span>to illustrate the strengths and weaknesses of the proposed method.</span>