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Asymptotic Error Expansions for Spline Interpolation

Published online by Cambridge University Press:  20 November 2018

H. P. Dikshit ,
A. Sharma  and
J. Tzimbalario
H. P. Dikshit
Affiliation:
University of AlbertaEdmonton, Alberta T6G2H1., Canada
A. Sharma
Affiliation:
University of AlbertaEdmonton, Alberta T6G2H1., Canada
J. Tzimbalario
Affiliation:
University of AlbertaEdmonton, Alberta T6G2H1., Canada
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Abstract

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During the last decade or so there has been a revival of interest in the analysis of error-bounds f(s)-S(s) for different classes of functions and their interpolatory splines of odd degree on a finite interval with variations on end conditions. Our object is to present a unified treatment of the asymptotic error expansion both for even and for odd degree interpolatory splines.

Keywords

41A60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 337 - 344
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Birkhoff, G. and De Boor, C., Error bounds for spline interpolation, J. Math. Mech., 13 (1964), 827–836.Google Scholar
2. Hansen, E. R., A Table of Series and Products, Prentice-Hall, 1975.Google Scholar
3. Kamerer, W. J., Reddien, G. W. and Varga, R. S., Quadratic interpolatory spline, Numer. Math., 22 (1974), 241–259.Google Scholar
4. Kershaw, D., A bound on the inverse of a band matrix which occurs in interpolation by periodic odd order splines, J. Inst. Maths. Applies, 20 (1977), 227–228.Google Scholar
5. Lucas, T. R., Asymptotic expansions for interpolating periodic splines, SIAM J. Numer. Anal., 19 (1982), 1051–1066.Google Scholar
6. Marsden, M., Quadratic spline interpolation, Bull. Amer. Math. Soc, 80 (1974), 903–906.Google Scholar
7. Schoenberg, I. J., Cardinal spline interpolation, SIAM Regional Conf. Series, 12 (1973).Google Scholar