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

Class GaussChebyshevQuadrature

java.lang.Object

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

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

All Implemented Interfaces:

Integrator

public class GaussChebyshevQuadrature
extends GaussianQuadrature

Gauss-Chebyshev Quadrature uses the following weighting function: \[ w(x) = \frac{1}{\sqrt{1 - x^2}} \] to evaluate integrals in the interval (-1, 1). Therefore, this method can be used for finding the integral \[ \int_{-1}^{+1} \frac {f(x)} {\sqrt{1 - x^2} }\,dx. \]

This results in the evaluation points being roots of Chebyshev polynomials. In this method, both the coefficients and the evaluation points can be calculated directly.

See Also:

Wikipedia: Chebyshev-Gauss quadrature

Constructor Summary

Constructors

Constructor and Description
GaussChebyshevQuadrature(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

GaussChebyshevQuadrature

public GaussChebyshevQuadrature(int n)

Create an integrator of order n.

Parameters:

n - the number of points in the quadrature rule