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.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1987
Accession Number
ADA181478

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Underwater Systems Center

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Amplitude Modulation
  • Astronomy
  • Australia
  • Canada
  • Classification
  • Frequency
  • Frequency Modulation
  • Military Research
  • Modulation
  • Naval Intelligence
  • Polynomials
  • Radio Astronomy
  • Rational Functions
  • Security
  • Signal Processing
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Theoretical Analysis.

Technology Areas

  • Space
  • Space - Space Objects