%0 Journal Article
%T A STABLE COUPLED NEWTON'S ITERATION FOR THE MATRIX INVERSE $P$-TH ROOT
%J International Journal of Mathematical Modelling & Computations
%I Islamic Azad University, Central tehran Branch
%Z 2228-6225
%A Sadeghi, Amir
%D 2015
%\ 03/21/2015
%V 5
%N 1 (WINTER)
%P 69-79
%! A STABLE COUPLED NEWTON'S ITERATION FOR THE MATRIX INVERSE $P$-TH ROOT
%K Inverse matrix pth roots
%K Coupled Newton's iterations
%K Convergency
%K Stability
%R
%X 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.
%U http://ijm2c.iauctb.ac.ir/article_521882_1dcc734aab3ddae6b987f1056e33dcda.pdf