Class GaussLegendre

java.lang.Object

org.episteme.core.mathematics.analysis.integration.GaussLegendre

public final class GaussLegendre
extends Object

Gauss-Legendre Quadrature.

Approximates integrals using roots of Legendre polynomials as nodes. Exact for polynomials of degree 2n-1.

* @author Silvere Martin-Michiellot

Reference:
Gauss, C. F. (1814). Methodus nova integralium valores per approximationem inveniendi. Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores.

Since:

1.0

Author:

Gemini AI (Google DeepMind)

Method Summary

Modifier and Type	Method	Description
static Real	integrate(Function<Real,Real> f, int n)	Computes the integral of f(x) over [-1, 1] using n points.
static Real	integrate(Function<Real,Real> f, Real a, Real b, int n)	Computes the integral of f(x) over [a, b] using n points.

Methods inherited from class Object

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

Method Details

integrate

public static Real integrate(Function<Real,Real> f,
 int n)

Computes the integral of f(x) over [-1, 1] using n points.

Parameters:

f - function to integrate

n - number of points

Returns:

integral value

integrate

public static Real integrate(Function<Real,Real> f,
 Real a,
 Real b,
 int n)

Computes the integral of f(x) over [a, b] using n points.

Performs change of variables from [-1, 1] to [a, b].

Parameters:

f - function to integrate

a - lower bound

b - upper bound

n - number of points

Returns:

integral value