More Numerically Accurate Algorithm for Stiff Matrix Exponential

Abstract

In this paper, we propose a novel, highly accurate numerical algorithm for matrix exponentials (MEs). The algorithm is based on approximating Putzer’s algorithm by analytically solving the ordinary differential equation (ODE)-based coefficients and approximating them. We show that the algorithm outperforms other ME algorithms for stiff matrices for several matrix sizes while keeping the computation and memory consumption asymptotically similar to these algorithms. In addition, we propose a numerical-error- and complexity-optimized decision tree model for efficient ME computation based on machine learning and genetic programming methods. We show that, while there is not one ME algorithm that outperforms the others, one can find a good algorithm for any given matrix according to its properties.