HermiteGF.jl Documentation

Stable evaluation of Gaussian radial basis functions using Hermite polynomials

Types

HermiteGF.Chebyshev — Type.

Chebyshev( xmin, xmax, nx )

Chebyshev nodes

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HermiteGF.Hermite — Type.

Hermite( nodes::NodesType, epsilon:Real, gamma:Real )

Hermite interpolation

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HermiteGF.Hermite — Method.

Hermite( xe )

This function returns the matrix He of the values of the HermiteGF basis functions. The computation is done via three term recurrence for Hermite functions with an argument gamma*x and then appropriate exponential scaling.

More details can be found in Section 5.1 of the paper

STABLE EVALUATION OF GAUSSIAN RADIAL BASIS FUNCTIONS USING HERMITE POLYNOMIALS by Anna Yurova and Katharina Kormann.

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HermiteGF.Radial — Type.

Radial( nodes::NodesType, epsilon, gamma )

Radial interpolation

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HermiteGF.Radial — Method.

Radial( xe )

returns evaluated function

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HermiteGF.Uniform — Type.

Uniform( xmin, xmax, nx )

Uniform nodes

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HermiteGF.InterpolationType — Type.

Interpolation type (Hermite or Radial)

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HermiteGF.NodesType — Type.

Node positions (Uniform or Chebyshev)

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