On the logarithms of matrices with central symmetry

Abstract

AbstractFor computing logarithms of a nonsingular matrix A, one well known algorithm named the inverse scaling and squaring method, was proposed by Kenney and Laub [14] for use with a Schur decomposition. In this paper we further consider (the computation of) the logarithms of matrices with central symmetry.We first investigate the structure of the logarithms of these matrices and then give the classifications of their logarithms. Then, we develop several algorithms for computing the logarithms. We show that our algorithms are four times cheaper than the standard inverse scaling and squaring method for matrices with central symmetry under certain conditions.