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Improved error bounds for scattered data interpolation by radial basis functions
Author(s):
R.
Schaback.
Journal:
Math. Comp.
68
(1999),
201-216.
MSC (1991):
Primary 41A15, 41A25, 41A30, 41A63, 65D10
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Abstract:
If additional smoothness requirements and boundary conditions are met, the well-known approximation orders of scattered data interpolants by radial functions can roughly be doubled.
References:
- 1.
- Ahlberg, J.H., Nilson, E.N. and Walsh, J.L. The theory of splines and their applications, Mathematics in Science and Engineering (38), Academic Press, 1967. MR 39:684
- 2.
- Iske, A. Characterization of function spaces associated with conditionally positive definite functions, Mathematical Methods for Curves and Surfaces, (M. Daehlen, T. Lyche and L.L. Schumaker, eds.), Vanderbilt University Press, Nashville, TN, pp. 265-270, 1995. MR 96f:65003
- 3.
- Iske, A. Reconstruction of functions from generalized Hermite-Birhoff data, Approximation Theory VIII, (C.K. Chui and L.L. Schumaker, eds.), World Scientific, Singapore, pp. 257-264, 1995. CMP 98:01
- 4.
- Madych, W.R. and Nelson, S.A. Error bounds for multiquadric interpolation, Approximation Theory VI (C.K. Chui and L.L. Schumaker and J.D. Ward, eds.), Academic Press, Boston, pp. 413-416, 1989. MR 91j:41002
- 5.
- Madych, W.R. and Nelson, S.A. Multivariate interpolation and conditionally positive definite functions. II, Math. Comp. 54 (1990), pp. 211-230. MR 90e:91007
- 6.
- Madych, W.R. and Nelson, S.A. Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation, Journal of Approximation Theory 70 (1992), pp. 94-114. MR 93f:41009
- 7.
- Schaback, R. Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics 3 (1995), pp. 251-264. MR 96a:41004
- 8.
- Schaback, R. and Wu, Z. Operators on radial functions, J. of Comp. and Appl. Math. 73 (1996), pp. 257-270. MR 97g:42002
- 9.
- Schumaker, L.L. Spline Functions: Basic Theory, Wiley-Interscience, 1981. MR 82j:41001
- 10.
- Wu, Z. and Schaback, R., Local error estimates for radial basis function interpolation of scattered data, IMA Journal of Numerical Analysis 13 (1993), pp. 13-27. MR 93m:65012
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Additional Information:
R.
Schaback
Affiliation:
Institut für Numerische und Angewandte Mathematik, Georg-August-Universität, Lotzestrasse 16-18, 37083, Göttingen, Germany
DOI:
10.1090/S0025-5718-99-01009-1
PII:
S 0025-5718(99)01009-1
Received by editor(s):
May 10, 1996
Received by editor(s) in revised form:
May 21, 1997
Copyright of article:
Copyright
1999,
American Mathematical Society
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