Characteristic matrices of layered periodic structures

Method of symmetric polynomials (MSP) is developed to calculations of high powers of matrices. It is based on the new type of recurrence relations between symmetric polynomials of n-th order. New algorithm for computation j-th power of matrix of order n is compared with methods of ordinary multiplication and repeated squaring of matrix. Dependencies of comparative effectiveness R of the new method from power j and order n of matrix are investigated. Computation matrix M2j by MSP is more effective and accurate than the method of repeated squaring of matrix if j > n, and with increasing j comparative effectiveness R tends to n/2.