Evaluation of Computing Symmetrical Zolotarev Polynomials of the First Kind

Abstract

This report summarize and compares with each other various methods for computing the symmetrical Zolotarev Polynomial of the first kind and its spectrum. Suitable criteria are suggested for the comparison. The best numerical stability shows the method employing Chebyshev polynomial recurrence. In case of the polynomial spectrum computation the best method is the one using the difference backward recursion introduced by M. Vlcek. Both methods are able to generate the polynomial of high degree up to, at least, 2000, using 32-bit IEEE floating point arithmetics.