Class GaussHermiteQuadrature

  • All Implemented Interfaces:
    Integrator

    public class GaussHermiteQuadrature
    extends GaussianQuadrature
    Gauss-Hermite quadrature exploits the fact that quadrature approximations are open integration formulas (that is, the values of the endpoints are not required) to evaluate of integrals in the range \((-\infty, \infty )\).

    The weighting function in this case is \(\exp(-x^2)\), which results in the evaluation points being roots of Hermite polynomials.

    Therefore, the method can be used for finding the integral \[ \int_{-\infty}^{+\infty} e^{-x^2} f(x)\,dx. \]

    See Also:
    Wikipedia: Gauss-Hermite quadrature
    • Constructor Detail

      • GaussHermiteQuadrature

        public GaussHermiteQuadrature​(int n)
        Create an integrator of order n.
        Parameters:
        n - the number of points in the quadrature rule