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

Authors:
Mary Shaw;J. F. Traub
Affiliations:
Department of Computer Science, Carnegie-Mellon University, Schenley Park, Pittsburgh, PA;Department of Computer Science, Carnegie-Mellon University, Schenley Park, Pittsburgh, PA
Venue:
Journal of the ACM (JACM)
Year:
1974

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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 3n - 2 multiplications. The best previous result required 1/2n(n + 1) multiplications. Some optimality results are presented.