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BIT Numerical Mathematics

, Volume 13, Issue 3, pp 338–343 | Cite as

Error estimates of Hermite interpolation

  • R. D. Riess
Article
  • 81 Downloads

Abstract

This paper presents a procedure for obtaining error estimates for Hermite interpolation at the Chebyshev nodes {cos ((2j+1)π/2n)} j =0n−1 −1≦x≦1, for functionsf(x) of various orders of continuity. The procedure is applicable in many cases when the usual Lagrangian error bound is not, and is a better bound, in general, when both are applicable.

Keywords

Hermite interpolation Chebyshev order of continuity 

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References

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    E. W. Cheney,Introduction to Approximation Theory, McGraw-Hill, New York, 1966.Google Scholar
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    P. J. Davis,Interpolation and Approximation, Blaisdell, Waltham, 1963.Google Scholar
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    G. Meinardus,Approximation of Functions: Theory and Numerical Methods, Springer, New York, 1967.Google Scholar
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    I. P. Natanson,Constructive Function Theory, Vol. 1. Ungar, New York, 1964.Google Scholar
  5. 5.
    G. Sansone,Orthogonal Functions, Interscience, New York, 1959.Google Scholar

Copyright information

© BIT Foundations 1973

Authors and Affiliations

  • R. D. Riess
    • 1
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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