A note on 'efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments' by A.H. Nuttall

Abstract

A.H. Nuttall's (see ibid., vol. ASSP-35, no.10, p.1486-7, 1987) algorithm for the evaluation of a polynomial at a large number of arguments is addressed. The authors supplement Nuttall's treatment of the problem by (1) giving a relationship between the coefficients of the original polynomial and those of the equivalent one in terms of the integer variable n and (2) by deriving a formula for the computation of the initial values required for Nuttall's recursive procedure to commence. As a result of these supplements, the recursive algorithm is completely programmable and can be efficiently implemented for any order N of the polynomial. Some general observations are made on the computational complexity in recursive evaluation in contrast to direct evaluation of a polynomial.