Aggressively truncated Taylor series method for accurate computation of exponentials of essentially nonnegative matrices (Q2923346)

This paper deals with the computation of the exponential of an essentially nonnegative matrix. By coupling Taylor series approximation with the scaling and squaring technique, new algorithms are proposed. An a priori componentwise relative error bound of truncation is established and based on it, a strategy is suggested to choose the order of series expansion and the scale factor so that the exponential can be computed with the desired relative accuracy.