An improved algorithm to compute the exponential of a matrix
For numerical computing practitioners, this offers a faster method for matrix exponential computation, a core operation in many scientific and engineering applications.
The authors present a new algorithm for computing the matrix exponential that reduces the number of matrix multiplications compared to the standard Patterson-Stockmeyer method, achieving 10-30% performance improvement over Padé approximants for a range of matrix norms.
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.