Methods of evaluating polynomial approximations in function evaluation routines

Abstract

The Editors of the Algorithms and Numerical Analysis departments of the CACM wish to encourage the submission of algorithms with supporting numerical analysis papers and numerical analysis papers with related algorithnis.Hence contributions are solicited consisting of a paper plus an algorithm. If accepted, the algorithm will appear in the Algorithms department and the paper will appear in the Numerical Analysis department.The ground rules are as follows: 1. The "paper-algorithm" should be submitted in duplicate to the editor of either one of the two departments. The covering letter should state that this is a joint contribution.2. Referees will be chosen for the algorithm and for the numerical analysis paper by the respective responsible editors. The algorithm and the paper will be refereed according to the standards of the appropriate department.3. After both the algorithm and the paper have been accepted by the respective editors, both will appear in the same issue of the CACJM, each with reference to the other.^J . 1' ". THAUB AND J. G. HEERIOT

A Simple Test Qualifying the Accuracy of Horner'S Rule for Polynomials

“…The first one is used for the approximation to the elementary functions [5]. The second one is due to Fike [9]. We answer questions relative to Horner's rule modified for a pipelined processor and we raise a new question relative to the argument reduction step.…”

Provably faithful evaluation of polynomials

“…The following polynomial is given in [10], where it is used as an approximation in IEEE single precision of 2…”