Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Efficiency of Chebyshev Approximation on Finite Subsets

Efficiency of Chebyshev Approximation on Finite Subsets E f f i c i e n c y of C h e b y s h e v CHARLES B. Approximation on Finite Subsets DUNHAM The University of Western Ontario, London, Ontario, Canada ABSTRACT. Chebyshev approximation on an interval and closed subsets by a Haar subspace are considered. The closeness of best approximations on subsets to the best approximation on the interval is examined. It is shown that under favorable conditions the difference is O((density of the subset)Z), making it unnecessary to use very large finite subsets to get good approximations on the interval. KEY WORDSANDPHRASES: Chebyshev approximation, interval, finite subset, Haar subspace C R CATEGORIES.' 5.13 1. Introduction Let X be a closed finite interval [o~, ~] and Y be a closed subset of X. Let C (X) be the space of continuous functions on X. For h E C(X) define II h IIr = sup [I h(x) I : x E Y}, II h II = II ~ II~, Let G be an n-dimensional subspace of C (X) satisfying the H a a r condition. The approximation problem on Y is given f E C ( X ) to find g* E G to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

Efficiency of Chebyshev Approximation on Finite Subsets

Journal of the ACM (JACM) , Volume 21 (2) – Apr 1, 1974

Loading next page...
 
/lp/association-for-computing-machinery/efficiency-of-chebyshev-approximation-on-finite-subsets-fWl1I33zEQ

References (6)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1974 by ACM Inc.
ISSN
0004-5411
DOI
10.1145/321812.321825
Publisher site
See Article on Publisher Site

Abstract

E f f i c i e n c y of C h e b y s h e v CHARLES B. Approximation on Finite Subsets DUNHAM The University of Western Ontario, London, Ontario, Canada ABSTRACT. Chebyshev approximation on an interval and closed subsets by a Haar subspace are considered. The closeness of best approximations on subsets to the best approximation on the interval is examined. It is shown that under favorable conditions the difference is O((density of the subset)Z), making it unnecessary to use very large finite subsets to get good approximations on the interval. KEY WORDSANDPHRASES: Chebyshev approximation, interval, finite subset, Haar subspace C R CATEGORIES.' 5.13 1. Introduction Let X be a closed finite interval [o~, ~] and Y be a closed subset of X. Let C (X) be the space of continuous functions on X. For h E C(X) define II h IIr = sup [I h(x) I : x E Y}, II h II = II ~ II~, Let G be an n-dimensional subspace of C (X) satisfying the H a a r condition. The approximation problem on Y is given f E C ( X ) to find g* E G to

Journal

Journal of the ACM (JACM)Association for Computing Machinery

Published: Apr 1, 1974

There are no references for this article.