a stable coupled newton's iteration for the matrix inverse $p$-th root

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.