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

Author

Young Researcher Club, Shahre-rey branch, Islamic Azad university, Tehran, Iran. Iran, Islamic Republic of

Abstract

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

Keywords