Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

A combined Remes-differential correction algorithm for rational approximation


Authors: Edwin H. Kaufman, David J. Leeming and G. D. Taylor
Journal: Math. Comp. 32 (1978), 233-242
MSC: Primary 41A50
MathSciNet review: 0460989
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a hybrid Remes-differential correction algorithm for computing best uniform rational approximants on a compact subset of the real line is developed. This algorithm differs from the classical multiple exchange Remes algorithm in two crucial aspects. First of all, the solving of a nonlinear system to find a best approximation on a given reference set in each iteration of the Remes algorithm is replaced with the differential correction algorithm to compute the desired best approximation on the reference set. Secondly, the exchange procedure itself has been modified to eliminate the possibility of cycling that can occur in the usual exchange procedure. This second modification is necessary to guarantee the convergence of this algorithm on a finite set without the usual normal and sufficiently dense assumptions that exist in other studies.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 41A50

Retrieve articles in all journals with MSC: 41A50


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0460989-8
Article copyright: © Copyright 1978 American Mathematical Society