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Approximation orders for natural splines in arbitrary dimensions
Author(s):
Tim
Gutzmer;
Jens
Markus
Melenk.
Journal:
Math. Comp.
70
(2001),
699-703.
MSC (2000):
Primary 41A15;
Secondary 41A63, 41A25
Posted:
October 18, 2000
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Abstract:
Based on variational properties, we generalize the approximation properties of the univariate natural cubic spline to splines in arbitrary dimensions.
References:
-
- 1.
- Adams, R.A. Sobolev Spaces. 1975 San Diego: Academic Press. MR 56:9247
- 2.
- Atteia, M. Fonctions ``spline'' et noyaux reproduisants d'Aronszajn-Bergman. R.A.I.R.O. 4 (1970), 31-43. MR 45:9109
- 3.
- Brenner, S.C., Scott, L.R. The Mathematical Theory of Finite Element Methods. 1994 New York: Springer. MR 95f:65001
- 4.
- Deny, J., Lions, J.-L. Les espaces du type de Beppo Levi. Ann. Inst. Fourier 5 (1954), 305-370. MR 17:646a
- 5.
- Duchon, J. Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. R.A.I.R.O. Analyse numérique 10 (1976), 5-12. MR 57:10315
- 6.
- Duchon, J. Sur l'erreur d'interpolation des fonctions de plusieurs variables par les
-splines. R.A.I.R.O. Analyse numérique 12 (1978), 325-334. MR 80j:41052 - 7.
- Meinguet, J. Multivariate interpolation at arbitrary points made simple. Journal of Applied Mathematics and Physics (ZAMP) 30 (1979), 292-304. MR 81e:41014
- 8.
- Powell, M.J.D. The uniform convergence of thin plate spline interpolation in two dimensions. Numerische Mathematik 68 (1994), 107-128. MR 95c:41037
- 9.
- Schaback, R. Radial basis functions viewed from cubic splines. Proceedings of Mannheim Conference 1996 (Nürnberger G., Schmidt J.W., Walz G., eds). 1997 Basel: Birkhäuser. MR 98h:41012
- 10.
- Schaback, R. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp. 68 (1999) 201-216. MR 99d:41037
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Additional Information:
Tim
Gutzmer
Affiliation:
Seminar für Angewandte Mathematik, ETH Zürich, CH-8092 Zürich
Email:
TGUTZMER@sairgroup.com
Jens
Markus
Melenk
Affiliation:
Seminar für Angewandte Mathematik, ETH Zürich, CH-8092 Zürich
Email:
melenk@sam.math.ethz.ch
DOI:
10.1090/S0025-5718-00-01299-0
PII:
S 0025-5718(00)01299-0
Keywords:
Multivariate interpolation
Received by editor(s):
July 13, 1999
Posted:
October 18, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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