com.numericalmethod.suanshu.analysis.integration.univariate.riemann
Class Romberg

java.lang.Object
  com.numericalmethod.suanshu.analysis.integration.univariate.riemann.Romberg

All Implemented Interfaces:

Integrator

public class Romberg
extends java.lang.Object
implements Integrator

Romberg's method computes an integral by generating a sequence of estimations of the integral values and then extrapolation. The estimations are extrapolated to where the discretization is 0.

For example, Simpson's rule is a special case of Romberg's method, with the number of points for extrapolation is equal to 2.

This implementation does not assume any particular integrator, other than that the integrator is an IterativeIntegrator. The user may combine Romberg's method with his favorite iterative integrator.

See Also:

Wikipedia: Romberg's method

Constructor Summary

Romberg(IterativeIntegrator integrator)
Construct an integrator by extending an IterativeIntegrator using Romberg's method.

Method Summary

double	integrate(UnivariateRealFunction f, double a, double b) Integrate function f from a to b.
double	precision() Get the convergence threshold.

Methods inherited from class java.lang.Object

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

Constructor Detail

Romberg

public Romberg(IterativeIntegrator integrator)

Construct an integrator by extending an IterativeIntegrator using Romberg's method.

Note that the iterative integrator must do at least 2 steps in order to carry out any extrapolation.

Parameters:

integrator - an iterative integrator

Method Detail

integrate

public double integrate(UnivariateRealFunction f,
                        double a,
                        double b)

Description copied from interface: Integrator

Integrate function f from a to b.

 / b
 |   f(x) dx
 / a
 

Specified by:

integrate in interface Integrator

Parameters:

f - a univariate function

a - lower limit

b - upper limit

Returns:

Σ(f(x))

precision

public double precision()

Description copied from interface: Integrator

Get the convergence threshold. The usage depends on the specific integrator.

For example, for an IterativeIntegrator, the integral is considered converged if the relative error of two successive sums is less than the threshold.

Specified by:

precision in interface Integrator

Returns:

the precision