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Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

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 | References | Similar articles | Additional information

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 $D^m$-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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