On the calculation of matrix exponential of a large order

Three approaches to calculating exponential of a matrix A = ||agh|| of order n are considered: the approximation of the Taylor expansion, the method of polynomials of principal minors (PPM), and approximation by means of PPM. This methods are used in combination with scaling and squaring, if max|agh| < 2/(n + 4). A comparison of above methods with Padé approximation is done. A new method for estimating the accuracy of calculations of the elements of a matrix exponential is proposed. It is based on the relative errors of the calculation of the maximum modulo element of the matrix expA.