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Interpolation, Method -> "RBF"

Interpolation[funcvaluelist,Method→"RBF",(options)] represents a way to perform interpolation utilizing radial basis functions when funcvaluelist is a list of scattered control points together with the function values in these points.
  • To use Interpolation, Method→"RBF", you first need to load the Obtuse Package using Needs["Obtuse`"].
  • If the calculated distances are Integer or Rational numbers, they will be converted to machine-number precision Real numbers. If you want some other precision, choose an appropriate function as setting for the DistanceFunction option
  • The following options can be given:
DistanceFunctionAutomaticdistance function to use in calculation of the distance matrix and the calculation of the distance from the interpolation point to the control points. Note, that the function here is expected to return the square of the distance
RadialBasisFunctionAutomaticRadial Basis Function required by the RBF interpolation method
EXAMPLESCLOSE ALL
Basic Examples   (2)
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Some 2D points:
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Add function values in the 2D point table:
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Test interpolation in one point:
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Check with the original function in the same point:
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If the same interpolation should be used in many different points, the function can be precompiled without specifying in which point it will be used. Note, in the plot below, that extrapolation is used along the border of the plot. As seen, this method has in this case strong predictive capability also for extrapolation.
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Let us check a 1D case:
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Some 1D points:
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Add function values in the point table:
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