An error analysis for radial basis function interpolation
Tóm tắt
Radial basis function interpolation refers to a method of interpolation which writes the interpolant to some given data as a linear combination of the translates of a single function ϕ and a low degree polynomial. We develop an error analysis which works well when the Fourier transform of ϕ has a pole of order 2m at the origin and a zero at ∞ of order 2κ. In case 0≤m≤κ, we derive error estimates which fill in some gaps in the known theory; while in case m>κ we obtain previously unknown error estimates. In this latter case, we employ dilates of the function ϕ, where the dilation factor corresponds to the fill distance between the data points and the domain.
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