Accession Number : ADA181478

Title :   Efficient Evaluation of Polynomials and Exponentials of Polynomials for Equi-Spaced Arguments.

Descriptive Note : Technical rept.,

Corporate Author : NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB

Personal Author(s) : Nuttall,Albert H

PDF Url : ADA181478

Report Date : 01 Apr 1987

Pagination or Media Count : 16

Abstract : The evaluation of polynomials at equi-spaced arguments is a recurring task that arises in many applications. When a k-th order polynomial is written in nested form, its evaluation generally requires k additions and k multiplications at each argument of interest. For a set of equi-spaced arguments, it is demonstrated that the multiplications can be entirely circumvented (except during initialization) and that a recursive procedure employing only k additions per stage will suffice to generate the sequence of polynomial values. For an exponential of polynomial, an even greater savings is possible; namely, the exponential can be circumvented (except during initialization), and only k multiplications per stage are required in a recursive procedure. Memory storage is also kept at a minimum.

Descriptors :   *POLYNOMIALS, *RECURSIVE FUNCTIONS, EFFICIENCY, EXPONENTIAL FUNCTIONS, MEMORY DEVICES, SEQUENCES, STORAGE, FREQUENCY MODULATION, LINEAR SYSTEMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE