Symmetric polynomials in the transfer matrix scaling

Abstract

The new method of the matrix exponential exp (Wz) computation is based on the use of symmetric polynomials of n-th order in combination with scaling matrix W. Calculation algorithm uses a new type of recurrence relations, which were obtained for symmetric polynomials. Evaluation of the scaling parameter, which provides a reliable calculation of the matrix exponential with admissible truncation error, is made. Method of minimizing roundoff errors in the calculation of high powers of matrices is suggested.