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

Class GaussLaguerreQuadrature

java.lang.Object

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

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

All Implemented Interfaces:

Integrator

public class GaussLaguerreQuadrature
extends GaussianQuadrature

Gauss-Laguerre quadrature exploits the fact that quadrature approximations are open integration formulas (i.e. the values of the endpoints are not required) to evaluate of integrals in the range \([0, \infty )\).

The choice of weighting function \(\exp(-x)\) results in the evaluation points being the roots of Laguerre Polynomials, which have to be found numerically.

Therefore, this method is useful for finding the integral \[ \int_0^\infty f(x) e^{-x} \, dx. \]

See Also:

Wikipedia: Gauss-Laguerre quadrature

Constructor Summary

Constructors

Constructor and Description
GaussLaguerreQuadrature(int n, double precision) 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

GaussLaguerreQuadrature

public GaussLaguerreQuadrature(int n,
                               double precision)

Create an integrator of order n.

Parameters:

n - the number of points in the quadrature rule

precision - the precision of the estimates of the coefficients