A comparison of radial basis functions
A.I. Rozhenko
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
Keywords: сплайн, алгоритм, радиальная базисная функция, воспроизводящее ядро, тренд, внешний дрейф, интерполяция, сглаживание, регрессия, сплайн с натяжением, регуляризованный сплайн, spline, algorithm, radial basis function, reproducing kernel, trend, external drift, interpolation, smoothing, regression, tension spline, regularized spline
Abstract
A survey of algorithms for approximation of multivariate functions with radial basis functions (RBF) splines is presented. Algorithms of interpolation, smoothing, selecting the smoothing parameter, and regression with splines are described in detail. These algorithms are based on the properties of conditional positive definiteness of the spline radial basis function. Several families of the radial basis functions generated by means of conditionally complete monotone functions are considered. Recommendations for the selection of the spline basis and on the preparation of the initial data for approximation with the help of the RBF spline are given.
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