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A new class of radial basis functions with compact support
Author(s):
M.
D.
Buhmann.
Journal:
Math. Comp.
70
(2001),
307-318.
MSC (2000):
Primary 41A05, 41A15, 41A25, 41A30, 65D05, 65D15
Posted:
March 16, 2000
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Abstract:
Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier in the literature.
References:
-
- [1]
- Buhmann, M.D. (1989) ``Cardinal interpolation with radial basis functions: an integral transform approach'', in Multivariate Approximation Theory IV, Walter Schempp, Karl Zeller, eds., International Series of Numerical Mathematics Vol. 90, Birkhäuser Verlag (Basel), pp. 41-64. MR 90m:41004
- [2]
- Buhmann, M.D. and C.A. Micchelli (1991) ``Multiply monotone functions for cardinal interpolation'', Advances in Appl. Math. 12, 358-386. MR 92g:41002
- [3]
- Buhmann, M.D. (1998) ``Radial basis functions on compact support'', Proceedings of the Edinburgh Math. Society 41, 33-46. MR 99d:41005
- [4]
- Gasper, G. (1975) ``Positive integrals of Bessel functions'', SIAM J. Math. Anal. 6, 868-881. MR 52:11144
- [5]
- Gradsteyn, I.S. and I.M. Ryzhik (1980) Table of Integrals, Series, and Products, Academic Press, San Diego. MR 81g:33001
- [6]
- Micchelli, C.A. (1986) ``Interpolation of scattered data: distance matrices and conditionally positive definite functions'', Constructive Approx. 2, 11-22. MR 88d:65016
- [7]
- Misiewicz, J.K. and D. St.P. Richards (1994) ``Positivity of integrals of Bessel functions'', SIAM J. Math. Anal. 25, 596-601. MR 95i:33004
- [8]
- Narcowich, F. and J. Ward (1991) ``Norms of inverses and condition numbers for matrices associated with scattered data'', J. Approx. Th. 64, 84-109. MR 92b:65017
- [9]
- Powell, M.J.D. (1992) ``The theory of radial basis function approximation in 1990'', in Advances in Numerical Analysis II, W.A. Light, ed., Claredon Press, Oxford, pp. 105-210. MR 95c:41003
- [10]
- Schaback, R. and Z. Wu (1996) ``Operators on radial functions'', J. of Computational and Appl. Math. 73, 257-270. MR 97g:42002
- [11]
- Stein, E. and G. Weiss (1971) Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton. MR 46:4102
- [12]
- Stewart, J. (1976) ``Positive definite functions and generalizations, an historical survey'', Rocky Mountains Math. J. 6, 409-434. MR 55:3679
- [13]
- Wendland, H. (1995) ``Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree'', Advances in Computational Mathematics 4, 389-396. MR 96h:41025
- [14]
- Wendland, H. (1997) ``Sobolev-type error estimates for interpolation by radial basis functions'', in Surface Fitting and Multiresolution Methods, A. LeMéhauté and L.L. Schumaker, eds., Vanderbilt University Press, Nashville, pp. 337-344. MR 99j:65012
- [15]
- Wendland, H. (1998) ``Error estimates for interpolation by radial basis functions of minimal degree, J. Approx. Th. 93, 258-272. MR 99g:65015
- [16]
- Williamson, R.E. (1956) ``Multiply monotone functions and their Laplace transforms'', Duke Math. J. 23, 189-207. MR 17:1061d
- [17]
- Wu, Z. and R. Schaback (1993) ``Local error estimates for radial basis function interpolation of scattered data'', IMA J. Numer. Anal. 13, 13-27. MR 93m:65012
- [18]
- Wu, Z. (1995) ``Compactly supported positive definite radial functions'', Advances in Computational Mathematics 4, 283-292. MR 97g:65031
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Additional Information:
M.
D.
Buhmann
Affiliation:
Lehrstuhl VIII Mathematik, Universität Dortmund, 44221 Dortmund, Germany
Address at time of publication:
Lehrstuhl Numerik, Justus-Liebig-Universität, Heinrich-Buff-Ring 44, 35392 Giessen, Germany
Email:
martin.buhmann@math.uni-giessen.de
DOI:
10.1090/S0025-5718-00-01251-5
PII:
S 0025-5718(00)01251-5
Received by editor(s):
January 7, 1999
Posted:
March 16, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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