Theoretical and numerical considerations about Padé approximants for the matrix logarithm

Abstract

We show that for a vast class of matrix Lie groups, which includes the orthogonal and the symplectic, diagonal Padé approximants of log((1+x)/(1-x)) are structure preserving. The conditioning of these approximants is analyzed. We also present a new algorithm for the Briggs-Padé method, based on a strategy for reducing the number of square roots in the inverse scaling and squaring procedure.