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Comparison of Radial Basis Functions

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Abstract

A survey of algorithms for approximation of multivariate functions with radial basis function (RBF) splines is presented. Algorithms of interpolating, smoothing, selecting the smoothing parameter, and regression with splines are described in detail. These algorithms are based on the feature of conditional positive definiteness of the spline radial basis function. Several families of radial basis functions generated by means of conditionally completely monotone functions are considered. Recommendations for the selection of the spline basis and preparation of initial data for approximation with the help of the RBF spline are given.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    A. I. Rozhenko

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  1. A. I. Rozhenko
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Correspondence to A. I. Rozhenko.

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Original Russian Text © A.I. Rozhenko, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 3, pp. 273–290.

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Rozhenko, A.I. Comparison of Radial Basis Functions. Numer. Analys. Appl. 11, 220–235 (2018). https://doi.org/10.1134/S1995423918030047

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  • DOI: https://doi.org/10.1134/S1995423918030047

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