Polynomial approximation errors for functions of low-order continuity

D. Elliott, P.J. Taylor

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

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Keywords

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

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