Polynomial approximation errors for functions of low-order continuity

D. Elliott; P.J. Taylor

doi:10.1007/BF01888164

Polynomial approximation errors for functions of low-order continuity

D. Elliott, P.J. Taylor

Electronic And Electrical Engineering

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Abstract

Given a function f defined on [-1, 1] we obtain, in terms of (n+1)st divided differences, expressions for the minimax error E n(f) and the error S n(f) obtained by truncating the Chebyshev series off after n+1 terms. The advantage of using divided differences is that f is required to have no more than a continuous second derivative on [-1, 1].

Original language	English
Pages (from-to)	381-387
Number of pages	6
Journal	Constructive Approximation
Volume	7
Issue number	1
DOIs	https://doi.org/10.1007/BF01888164
Publication status	Published - Dec 1991

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Keywords

divided differences
minimax error
truncated Chebyshev series
Chebyshev coefficient

Cite this

Elliott, D., & Taylor, P. J. (1991). Polynomial approximation errors for functions of low-order continuity. Constructive Approximation, 7(1), 381-387. https://doi.org/10.1007/BF01888164

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AB - Given a function f defined on [-1, 1] we obtain, in terms of (n+1)st divided differences, expressions for the minimax error E n(f) and the error S n(f) obtained by truncating the Chebyshev series off after n+1 terms. The advantage of using divided differences is that f is required to have no more than a continuous second derivative on [-1, 1].

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KW - minimax error

KW - truncated Chebyshev series

KW - Chebyshev coefficient

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Access to Document

10.1007/BF01888164

http://dx.doi.org/10.1007/BF01888164