Accession Number:

ADA009250

Title:

Analysis of a Family of Algorithms for the Evaluation of a Polynomial and Some of Its Derivatives,

Descriptive Note:

Corporate Author:

CARNEGIE INST OF TECH PITTSBURGH PA DEPT OF COMPUTER SCIENCE

Personal Author(s):

Report Date:

1975-02-26

Pagination or Media Count:

44.0

Abstract:

The authors have previously presented a new one parameter family of algorithms and a program for evaluating the first m derivatives of a polynomial of degree n. In this paper the authors analyze that family of algorithms and present practical algorithms for selecting optimal or good values of the parameter q. A program for selecting the optimal value of q under the constraint at q divides nl is given. The authors also analyze a program that eliminates that constraint and a simple program that selects a good, but not always optimal, value of q. Bounds are derived on how close to optimal the good value will be. The above results apply for n 12. The authors extend the results to all n by tabulating the cost function for n or 12.

Subject Categories:

  • Theoretical Mathematics
  • Computer Programming and Software

Distribution Statement:

APPROVED FOR PUBLIC RELEASE