Numerical Computation of the Matrix Exponential with Accuracy Estimate

This paper presents and analyzes an algorithm for computing the exponential of an arbitrary n n matrix. Diagonal Padé table approximations are used in conjunction with several techniques for reducing the norm of the matrix. An important feature of the algorithm is that an estimate for the minimum number of digits accurate in the norm of the computed exponential matrix is returned to the user. In obtaining this estimate, several interesting results concerning rounding errors and Padé approximations are presented.