Title

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

Date of Original Version

2-1975

Type

Technical Report

Rights Management

All Rights Reserved

Abstract or Description

We have previously presented a new one parameter family of algorithms and a program for evaluation the first m derivatives of a polynomial of degree n. In this paper we analyze that family of algorithms and present practical algorithms for selecting optimal or good values of the parameter q.

A program for selection the optimal value of q under the constraint that q divides n+1 is given. We also analyze a program that eliminates that constraint and a simple program that selects a good, but not always optimal, value of q. We derive bounds on how close to optimal the "good" value will be.

The above results apply for n >12. We extend the results to all n by tabulating the cost function for n ≤ 12.

Some open questions on extensions of our results are stated.

Comments

Carnegie-Mellon University Computer Science Technical Report, February 1975. A substantially abbreviated version appeared in Information Processing Letters, October 1977.

 

Published In

Carnegie-Mellon University Computer Science Technical Report.