Error analysis of the truncated Taylor series expansion method for computing matrix exponential

Abstract

In this paper, we perform an error analysis of the truncated Taylor series expansion method for computing matrix exponential by taking into account both the truncation error and the rounding error. The derived error bound will be useful to determine the order of expansion or computing precision required to attain the prespecified error level. We also consider mixed-precision computation and give a criterion to determine the order after which lower precision arithmetic can be used without affecting the overall accuracy.