Mollification formulas and implicit smoothing
R.K. Beatson and H.Q. Bui
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Abstract
This paper develops some mollification formulas involving convolutions between popular radial basis function (RBF) basic functions Φ, and suitable mollifiers k. Polyharmonic spline, scaled Bessel kernel (Matern function) and compactly supported basic functions are considered. A typical result relates powers of the modulus and generalised multiquadrics via the formula
An application which motivated the development of the formulas is a technique called implicit smoothing. This computationally efficient technique smooths a previously obtained RBF fit by replacing the basic function Φ with a smoother version Ψ during evaluation.
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