Method of symmetric polynomials in the computations of scattering matrix

The method for calculating any analytic matrix function by means of symmetric polynomials is presented. The method of symmetric polynomials (MSP) is applied to the calculation of the fundamental matrix of a differential equations system. The scaling method is developed for computation of the scattering matrix. An analytical estimate of the scaling parameter, allowing the calculation of the matrix exponential with the required reliability and accuracy is obtained. This parameter depends on the matrix order n, the value of the matrix elements and layer thickness.