RadialBasisFunction Class

public abstract class RadialBasisFunction : Curve

Public MustInherit Class RadialBasisFunction
	Inherits Curve

public ref class RadialBasisFunction abstract : public Curve

[<AbstractClassAttribute>]
type RadialBasisFunction = 
    class
        inherit Curve
    end

Inheritance

Object  →  Curve  →  RadialBasisFunction

This abstract base class represents a radial basis function kernel φ(r) where r ≥ 0 is the distance from a center point. RBF kernels are used in radial basis function interpolation to construct smooth approximations of scattered data.

Different kernels have different smoothness properties and may be more or less suitable depending on the application. Some kernels have compact support (non-zero only within a finite radius), while others have infinite support but decay to zero at infinity.

RBF kernels are classified as either strictly positive definite (PD) or conditionally positive definite (CPD). CPD kernels require polynomial augmentation during interpolation to ensure well-posedness and exact reproduction of low-degree polynomials.

To create standard RBF kernels, use the static factory class RadialBasisFunctions. Custom kernels can be implemented by deriving from this class.

Reference