Analysis of a Family of Algorithms for the Evaluation of a Polynomial and Some of Its Derivatives,
CARNEGIE INST OF TECH PITTSBURGH PA DEPT OF COMPUTER SCIENCE
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The authors 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 the authors analyze that family of algorithms and present practical algorithms for selecting optimal or good values of the parameter q. A program for selecting the optimal value of q under the constraint at q divides nl is given. The authors also analyze a program that eliminates that constraint and a simple program that selects a good, but not always optimal, value of q. Bounds are derived on how close to optimal the good value will be. The above results apply for n 12. The authors extend the results to all n by tabulating the cost function for n or 12.
- Theoretical Mathematics
- Computer Programming and Software