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