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

Class Midpoint

java.lang.Object

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

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

All Implemented Interfaces:

Integrator, IterativeIntegrator, java.io.Serializable

public class Midpoint
extends NewtonCotes

The midpoint rule computes an approximation to a definite integral, made by finding the area of a collection of rectangles whose heights are determined by the values of the function. Specifically, the interval over which the function is to be integrated is divided into equal subintervals of length. The rectangles are then drawn. The approximation to the integral is then calculated by adding up the areas (base multiplied by height) of the rectangles.

See Also:

Wikipedia: Rectangle method, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.NewtonCotes

NewtonCotes.Type

Constructor Summary

Constructors

Constructor and Description
Midpoint(double precision, int maxIterations) Construct an integrator that implements the Midpoint rule.

Method Summary

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

getMaxIterations, getPrecision, h, integrate, next

Methods inherited from class java.lang.Object

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

Constructor Detail

Midpoint

public Midpoint(double precision,
                int maxIterations)

Construct an integrator that implements the Midpoint rule.

Parameters:

precision - the convergence threshold

maxIterations - the maximum number of iterations