Polynomial approximation errors for functions of low-order continuity

D. Elliott, P.J. Taylor

Research output: Contribution to journal › Article

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)381-387
Number of pages6
JournalConstructive Approximation
Volume7
Issue number1
DOIs
Publication statusPublished - Dec 1991

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Order Continuity
Polynomial approximation
Divided Differences
Polynomial Approximation
Approximation Error
Chebyshev Series
Second derivative
Minimax
Derivatives
Term

Keywords

  • divided differences
  • minimax error
  • truncated Chebyshev series
  • Chebyshev coefficient

Cite this

Elliott, D. ; Taylor, P.J. / Polynomial approximation errors for functions of low-order continuity. In: Constructive Approximation. 1991 ; Vol. 7, No. 1. pp. 381-387.
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Elliott, D & Taylor, PJ 1991, 'Polynomial approximation errors for functions of low-order continuity', Constructive Approximation, vol. 7, no. 1, pp. 381-387. https://doi.org/10.1007/BF01888164

Polynomial approximation errors for functions of low-order continuity. / Elliott, D.; Taylor, P.J.

In: Constructive Approximation, Vol. 7, No. 1, 12.1991, p. 381-387.

Research output: Contribution to journal › Article

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

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