Mollification formulas and implicit smoothing.
Degree GrantorUniversity of Canterbury
Degree NameResearch Report UCDMS 2003/19
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. 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. In the case of the polyharmonic spline basic functions the smoothed basic function is a generalised multiquadric or shifted thin-plate spline (at least up to a polynomial).
SubjectsField of Research::01 - Mathematical Sciences::0103 - Numerical and Computational Mathematics::010301 - Numerical Analysis
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