Efficient Evaluation of Polynomials and Exponentials of Polynomials for Equi-Spaced Arguments.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1987
- Accession Number
- ADA181478
Entities
People
- Albert H. Nuttall
Organizations
- Naval Underwater Systems Center