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J. Rice (1964)
The approximation of functions
T. Rivlin, E. Cheney (1966)
A Comparison of Uniform Approximations on an Interval and a Finite Subset ThereofSIAM Journal on Numerical Analysis, 3
L. Goddard (1965)
Approximation of FunctionsNature, 205
J. Peetre (1970)
Approximation of normsJournal of Approximation Theory, 3
(1961)
Journal of the Association for Computing MachineryNature, 190
Note. Reference [4] is not cited in the text
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 of the ACM (JACM) – Association for Computing Machinery
Published: Apr 1, 1974
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