An improved algorithm to compute the exponential of a matrix

2017/10/30 by Bader, Philipp, Blanes, Sergio, Casas, Fernando
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1710.10989

Abstract

In this work, we present a new way to compute the Taylor polynomial of the matrix exponential which reduces the number of matrix multiplications in comparison with the de-facto standard Patterson-Stockmeyer method. This reduction is sufficient to make the method superior in performance to Padé approximants by 10-30% over a range of values for the matrix norms and thus we propose its replacement in standard software kits. Numerical experiments show the performance of the method and illustrate its stability.

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