Roy, S. C. D. and Minocha, S.
(1991).
A note on 'Efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments' by A.H. Nuttall.
IEEE Transactions on Signal Processing, 39(11),
pp. 2554–2556.
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.
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