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Constructive Approximation

, Volume 7, Issue 1, pp 381–387 | Cite as

Polynomial approximation errors for functions of low-order continuity

  • David Elliott
  • Peter J. Taylor
Article

Abstract

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

AMS classification

41A10 41A50 42A15 42A16 

Key words and phrases

Divided differences Minimax error Truncated Chebyshev series Chebyshev coefficient 

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Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • David Elliott
    • 1
  • Peter J. Taylor
    • 2
  1. 1.Department of MathematicsUniversity of TasmaniaHobartAustralia
  2. 2.Department of MathematicsUniversity of StrathclydeGlasgowScotland

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