Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-16T19:29:16.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Schoenberg's exponential Euler spline curves*

Published online by Cambridge University Press:  14 November 2011

K. Jetter ,
S. D. Riemenschneider  and
N. Sivakumar
K. Jetter
Affiliation:
Fachbereich Mathematik, Universität Duisburg, Lotharstraße 65, 4100 Duisburg 1, Federal Republic of Germany
S. D. Riemenschneider
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G2G1, Canada
N. Sivakumar
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G2G1, Canada
Get access Rights & Permissions [Opens in a new window]

Synopsis

The exponential Euler spline curves of Schoenberg are used to derive the correctness of cardinal interpolation by shifted univariate B-splines and the “metric condition” on the bi-infinite Toeplitz matrix of interpolation. Additional monotonicity properties of the associated symbol for interpolation in each of its parameters are also given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 21 - 33
Copyright
Copyright © Royal Society of Edinburgh 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

4.References

1de Boor, C.. On the cardinal spline interpolant to e iut. SIAM J. Math. Anal. 7 (1976), 930–941.CrossRefGoogle Scholar
2de Boor, C. and Schoenberg, I. J.. Cardinal interpolation and spline functions VIII: The Budan-Fourier theorem for splines and applications. In Spline Functions, Karlsruhe 1975, eds Böhmer, K., Meinardus, G. and Schempp, W., Lecture Notes in Mathematics 501, pp. 1–79 (Berlin: Springer, 1976).Google Scholar
3Micchelli, C. A.. Cardinal L-splines. In Studies in Spline Functions and Applications, eds. Karlin, S. et al., pp. 203–250 (New York: Academic Press, 1976).Google Scholar
4Nörlund, N. E.. Vorlesungen über Differenzenrechnung (Berlin: Springer, 1924).CrossRefGoogle Scholar
5Schoenberg, I. J.. Cardinal interpolation and spline functions. J. Approxim. Theory 2 (1969), 167–206.CrossRefGoogle Scholar
6Schoenberg, I. J.. Cardinal Spline Interpolation (Philadelphia: SIAM, 1973).CrossRefGoogle Scholar
7Schoenberg, I. J.. Cardinal interpolation and spline functions IV: The exponential Euler spline. In Linear Operators and Approximation, eds Butzer, P. L., Kahane, J.-P., and Sz.-Nagy, B., ISBN 20, pp. 382–404 (Basel: Birkhauser, 1972).CrossRefGoogle Scholar
8Schoenberg, I. J.. A new approach to Euler splines. J. Approxim. Theory 39 (1983), 324–337.CrossRefGoogle Scholar
9Smith, P. and Ward, J.. Quasi-Interpolants from spline interpolation. Constr. Approx. 6 (1990), 97–110.CrossRefGoogle Scholar