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_roots_hermite_asy(n)

Computes the sample points and weights for Gauss-Hermite quadrature. The sample points are the roots of the nth degree Hermite polynomial, $H_n(x)$ . These sample points and weights correctly integrate polynomials of degree $2n - 1$ or less over the interval $[-\infty, \infty]$ with weight function $f(x) = e^{-x^2}$ .

This method relies on asymptotic expansions which work best for n > 150. The algorithm has linear runtime making computation for very large n feasible.

Parameters

n : int

quadrature order

Returns

nodes : ndarray

Quadrature nodes

weights : ndarray

Quadrature weights

Gauss-Hermite (physicist's) quadrature for large n.

See Also

roots_hermite

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.special._orthogonal._initial_nodes scipy.special._orthogonal._initial_nodes_a scipy.special._orthogonal._newton scipy.special._orthogonal._initial_nodes_b

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /scipy/special/_orthogonal.py#1188
type: <class 'function'>
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