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Radial basis functions
Abstract
Radial basis function methods are modern ways to approximate multivariate functions, especially in the absence of grid data. They have been known, tested and analysed for several years now and many positive properties have been identified. This paper gives a selective but up-to-date survey of several recent developments that explains their usefulness from the theoretical point of view and contributes useful new classes of radial basis function. We consider particularly the new results on convergence rates of interpolation with radial basis functions, as well as some of the various achievements on approximation on spheres, and the efficient numerical computation of interpolants for very large sets of data. Several examples of useful applications are stated at the end of the paper.
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Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
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Holden, M. (2008) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2007.904691 · Cited by 369
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Ghotra, B., McIntosh, S., & Hassan, A. E. (2015) · 2015 IEEE/ACM 37th IEEE International Conference on Software Engineering · doi:10.1109/icse.2015.91 · Cited by 364
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Bogomolov, A., Lepri, B., & Pianesi, F. (2013) · 2013 International Conference on Social Computing · doi:10.1109/socialcom.2013.118 · Cited by 67
Metadata
- Authors
- Buhmann, M. D.
- Venue
- Acta Numerica
- Publisher
- Cambridge University Press (CUP)
- Published
- 2000-01
- Volume
- 9
- Pages
- 1-38
- ISSN
- 0962-4929 (ISSN-L)
- 1474-0508
- OpenAlex
- W2107699930
- Cited by
- 1,654
- References
- 1
- FWCI
- 29.03
- Type
- journal article
- Language
- en
- Open access
- closed
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