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Cardinal Interpolation and Generalized Exponential Euler Splines

Published online by Cambridge University Press:  20 November 2018

A. Sharma  and
J. Tzimbalario
A. Sharma
Affiliation:
University of Alberta, Edmonton, Alberta
J. Tzimbalario
Affiliation:
University of Alberta, Edmonton, Alberta
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Let denote the class of cardinal splines S(x) of degree n (n ≧ 1) having their knots at the integer points of the real axis. We assume that the knots are simple so that . Recently Schoenberg [3] has studied cardinal splines such that S(x) interpolates the exponential function tx at the integers and

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 291 - 300
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Gelfond, A. E., Calculus of finite differences (Dunod, Paris, 1963.)Google Scholar
2. Greville, T. N. E., Schoenberg, I. J. and Sharma, A., The spline interpolation of sequences satisfying a linear recurrence relation (to appear).Google Scholar
3. Schoenberg, I. J., Cardinal interpolation and spline functions IV. The exponential Euler splines, appeared in Linear Operators and Approximation Theory Proc. of Conference in Oberwolfach Aug. 14-22, 1971, edited by Butzer, P. L., Kahane, J. P., B. Sz. Nagy, Birkhauser, Basel 1972, pp. 382–404.Google Scholar
4. Schoenberg, I. J., Cardinal spline interpolation, Regional Conference Series in Applied Mathematics No. 12 (S.I.A.M. Philadelphia 1973).Google Scholar