We 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 we analyze that family of algorithms and present practical algorithms for selecting optimal or good values of the parameternq.nA program for selecting 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.nThe above results apply for n > 12. We extend the results to all n by tabulating the cost function for n ≦ 12.nSome open questions on extensions of our results are stated.
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