• Analysis of a family of algori...

Treffer: Analysis of a family of algorithms for the evaluation of a polynomial and some of its derivatives

Title:
Analysis of a family of algorithms for the evaluation of a polynomial and some of its derivatives
Authors:
Mary Shaw, J. F.(Joseph Frederick) Traub
Publication Year:
2018
Collection:
KiltHub Research from Carnegie Mellon University
Subject Terms:
Other information and computing sciences not elsewhere classified, Numerical analysis Computer programs, Algorithms, Information and Computing Sciences not elsewhere classified
Document Type:
Fachzeitschrift article in journal/newspaper
Language:
unknown
Relation:
https://figshare.com/articles/journal_contribution/Analysis_of_a_family_of_algorithms_for_the_evaluation_of_a_polynomial_and_some_of_its_derivatives/6603464
DOI:
10.1184/r1/6603464.v1
Availability:
https://doi.org/10.1184/r1/6603464.v1
https://figshare.com/articles/journal_contribution/Analysis_of_a_family_of_algorithms_for_the_evaluation_of_a_polynomial_and_some_of_its_derivatives/6603464
Rights:
In Copyright
Accession Number:
edsbas.8D0778C7
Database:
BASE

Weitere Informationen

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 parameter q. A 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. The above results apply for n > 12. We extend the results to all n by tabulating the cost function for n≤12. Some open questions on extensions of our results are stated