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摘要
En 中文
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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