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Choice of Basis for Chebyshev Approximation

Choice of Basis for Chebyshev Approximation Choice of Basis for Chebyshev Approximation CHARLES B. DUNHAM University of Western Ontario, Canada In Chebyshev approximation on a finite interval by polynomials or ordinary rationals usmg the Fraser-Hart version of the Remez second algorithm, a choice of basis for polynomials must be made. The power basis and Chebyshev polynomial Tk basis are compared. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]" Approximation--Chebyshev approx~rnatmn and theory General Terms: Algorithms; Design Additional Key Words and Phrases: polynomials, rational functions, Fraser-Hart-Remez algorithm, condition numbers INTRODUCTION In polynomial C h e b y s h e v a p p r o x i m a t i o n on an interval b y the R e m e z algorithm, one can use a power basis or a C h e b y s h e v polynomial basis for polynomials. M o r e generally, in rational C h e b y s h e v a p p r o x i m a t i o n b y the F r a s e r - H a r t - R e m e z algorithm, one can use a power basis or a C http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

Choice of Basis for Chebyshev Approximation

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References (16)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1982 by ACM Inc.
ISSN
0098-3500
DOI
10.1145/355984.355987
Publisher site
See Article on Publisher Site

Abstract

Choice of Basis for Chebyshev Approximation CHARLES B. DUNHAM University of Western Ontario, Canada In Chebyshev approximation on a finite interval by polynomials or ordinary rationals usmg the Fraser-Hart version of the Remez second algorithm, a choice of basis for polynomials must be made. The power basis and Chebyshev polynomial Tk basis are compared. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]" Approximation--Chebyshev approx~rnatmn and theory General Terms: Algorithms; Design Additional Key Words and Phrases: polynomials, rational functions, Fraser-Hart-Remez algorithm, condition numbers INTRODUCTION In polynomial C h e b y s h e v a p p r o x i m a t i o n on an interval b y the R e m e z algorithm, one can use a power basis or a C h e b y s h e v polynomial basis for polynomials. M o r e generally, in rational C h e b y s h e v a p p r o x i m a t i o n b y the F r a s e r - H a r t - R e m e z algorithm, one can use a power basis or a C

Journal

ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery

Published: Mar 1, 1982

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