论文信息 - On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives

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

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

Mary Shaw | Joseph F. Traub | J. Traub | M. Shaw

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