DOI: 10.1090/s0025-5718-00-01251-5. A new class of radial basis functions with compact support

A new class of radial basis functions with compact support

10.1090/s0025-5718-00-01251-5

Crossref journal-article

American Mathematical Society (AMS)

Mathematics of Computation (14)

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.

Bibliography

Buhmann, M. (2000). A new class of radial basis functions with compact support. Mathematics of Computation, 70(233), 307â318. Portico.

Authors 1

M. Buhmann (first)

References 18 Referenced 98

{'key': '1', 'first-page': '41', 'article-title': 'Cardinal interpolation with radial basis functions: an integral transform approach', 'author': 'Buhmann, M. D.', 'year': '1989'} / Cardinal interpolation with radial basis functions: an integral transform approach by Buhmann, M. D. (1989)
10.1016/0196-8858(91)90018-E / Adv. in Appl. Math. / Multiply monotone functions for cardinal interpolation by Buhmann, Martin D. (1991)
10.1017/S0013091500019416 / Proc. Edinburgh Math. Soc. (2) / Radial functions on compact support by Buhmann, M. D. (1998)
10.1137/0506076 / SIAM J. Math. Anal. / Positive integrals of Bessel functions by Gasper, George (1975)
{'key': '5', 'isbn-type': 'print', 'volume-title': 'Table of integrals, series, and products', 'author': 'Gradshteyn, I. S.', 'year': '1980', 'ISBN': 'http://id.crossref.org/isbn/0122947606'} / Table of integrals, series, and products by Gradshteyn, I. S. (1980)
10.1007/BF01893414 / Constr. Approx. / Interpolation of scattered data: distance matrices and conditionally positive definite functions by Micchelli, Charles A. (1986)
10.1137/S0036141092226934 / SIAM J. Math. Anal. / Positivity of integrals of Bessel functions by Misiewicz, Jolanta K. (1994)
10.1016/0021-9045(91)90087-Q / J. Approx. Theory / Norms of inverses and condition numbers for matrices associated with scattered data by Narcowich, Francis J. (1991)
{'key': '9', 'series-title': 'Oxford Science Publications', 'isbn-type': 'print', 'volume-title': 'Advances in numerical analysis. Vol. II', 'year': '1992', 'ISBN': 'http://id.crossref.org/isbn/0198534396'} / Advances in numerical analysis. Vol. II / Oxford Science Publications (1992)
10.1016/0377-0427(96)00047-7 / J. Comput. Appl. Math. / Operators on radial functions by Schaback, Robert (1996)
{'key': '11', 'series-title': 'Princeton Mathematical Series, No. 32', 'volume-title': 'Introduction to Fourier analysis on Euclidean spaces', 'author': 'Stein, Elias M.', 'year': '1971'} / Introduction to Fourier analysis on Euclidean spaces / Princeton Mathematical Series, No. 32 by Stein, Elias M. (1971)
10.1216/RMJ-1976-6-3-409 / Rocky Mountain J. Math. / Positive definite functions and generalizations, an historical survey by Stewart, James (1976)
10.1007/BF02123482 / Adv. Comput. Math. / Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree by Wendland, Holger (1995)
{'key': '14', 'first-page': '337', 'article-title': 'Sobolev-type error estimates for interpolation by radial basis functions', 'author': 'Wendland, Holger', 'year': '1997'} / Sobolev-type error estimates for interpolation by radial basis functions by Wendland, Holger (1997)
10.1006/jath.1997.3137 / J. Approx. Theory / Error estimates for interpolation by compactly supported radial basis functions of minimal degree by Wendland, Holger (1998)
10.2307/1989990 / Trans. Amer. Math. Soc. / Steinitz field towers for modular fields by MacLane, Saunders (1939)
10.1093/imanum/13.1.13 / IMA J. Numer. Anal. / Local error estimates for radial basis function interpolation of scattered data by Wu, Zong Min (1993)
10.1007/BF03177517 / Adv. Comput. Math. / Compactly supported positive definite radial functions by Wu, Zong Min (1995)

Dates

Type	When
Created	20 years, 1 month ago (July 11, 2005, 5:02 p.m.)
Deposited	4 years ago (July 29, 2021, 8:23 p.m.)
Indexed	15 hours, 59 minutes ago (Aug. 21, 2025, 12:35 p.m.)
Issued	25 years, 5 months ago (March 16, 2000)
Published	25 years, 5 months ago (March 16, 2000)
Published Online	25 years, 5 months ago (March 16, 2000)

Funders 0

None

BibTeX

@article{Buhmann_2000, title={A new class of radial basis functions with compact support}, volume={70}, ISSN={1088-6842}, url={http://dx.doi.org/10.1090/s0025-5718-00-01251-5}, DOI={10.1090/s0025-5718-00-01251-5}, number={233}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Buhmann, M.}, year={2000}, month=mar, pages={307–318} }

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