Matrix exponential: Approximation by truncated power series

The solution of the linear, autonomous vector differential equation x = Fx at t = mT, where m is an integer, may be expressed in terms of the matrix exponential e
^FT
. The matrix exponential may be approximated conveniently by truncating its defining power series. A criterion for selecting the number of terms to be retained in the truncation is proposed. This criterion eliminates difficulties encountered in applying other recently proposed criteria.