com.numericalmethod.suanshu.analysis.integration.univariate.riemann.gaussian

Class GaussHermiteQuadrature

java.lang.Object

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.gaussian.GaussianQuadrature

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.gaussian.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 Summary

Constructors

Constructor and Description
GaussHermiteQuadrature(int n) Create an integrator of order n.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.gaussian.GaussianQuadrature

getPrecision, integrate

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GaussHermiteQuadrature

public GaussHermiteQuadrature(int n)

Create an integrator of order n.

Parameters:

n - the number of points in the quadrature rule