On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives-Reference-Cited by-同舟云学术

On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives

Published:1974-01 Issue:1 Volume:21 Page:161-167
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Shaw Mary¹,Traub J. F.¹

Affiliation:

1. Department of Computer Science, Carnegie-Mellon University, Schenley Park, Pittsburgh, PA

Abstract

A family of new algorithms is given for evaluating the first m derivatives of a polynomial. In particular, it is shown that all derivatives may be evaluated in 3 n - 2 multiplications. The best previous result required 1/2 n ( n + 1) multiplications. Some optimality results are presented.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/321796.321810

Reference8 articles.

1. HORNERS RULE IS UNIQUELY OPTIMAL

2. BORODIN A. Private communication. BORODIN A. Private communication.

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