net.sf.doodleproject.numerics4j.root
Class NewtonRootFinder

java.lang.Object
  net.sf.doodleproject.numerics4j.IterativeMethod
      net.sf.doodleproject.numerics4j.root.NewtonRootFinder

public class NewtonRootFinder
extends IterativeMethod

Newton's method (1) for finding roots of functions.

For example, to find roots for sine, first a Function is defined:

 Function sine = new Function() {
    public double evaluate(double x) {
        return Math.sin(x);
    }}
 };
 

along with its derivative:

 Function cos = new Function() {
    public double evaluate(double x) {
        return Math.cos(x);
    }}
 };
 

Then, a Newton's method root finder is created with the above function:

 NewtonRootFinder finder = new NewtonRootFinder(sine, cos);
 

Lastly, locating roots is accomplished using the findRoot(double) method:

 // find the root close to 3.
 double pi = finder.findRoot(3.0);
 
 // find the root between close to 1.
 double zero = finder.findRoot(1.0);
 

References:

1. Eric W. Weisstein. "Newton's Method." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NewtonsMethod.html

Since:

1.1

Version:

$Revision: 1.3 $ $Date: 2007/10/27 04:57:42 $

Constructor Summary

NewtonRootFinder(Function f, Function d)
Create a root finder for the given function.

NewtonRootFinder(Function f, Function d, int iterations, double error)
Create a root finder for the given function.

Method Summary

double	findRoot(double x) Find a root of the target function that lies close to x.
Function	getDerivative() Access the derivative of the target function.
Function	getFunction() Access the target function.
void	setDerivative(Function f) Modify the derivative of the target function.
void	setFunction(Function f) Modify the target function.

Methods inherited from class net.sf.doodleproject.numerics4j.IterativeMethod

getMaximumIterations, getMaximumRelativeError, iterate, setMaximumIterations, setMaximumRelativeError

Methods inherited from class java.lang.Object

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

Constructor Detail

NewtonRootFinder

public NewtonRootFinder(Function f,
                        Function d)

Create a root finder for the given function.

Parameters:

f - the target function.

d - the first derivative of f.

NewtonRootFinder

public NewtonRootFinder(Function f,
                        Function d,
                        int iterations,
                        double error)

Create a root finder for the given function.

Parameters:

f - the target function.

d - the first derivative of f.

iterations - maximum number of iterations.

error - maximum relative error.

Method Detail

findRoot

public double findRoot(double x)
                throws NumericException

Find a root of the target function that lies close to x.

Parameters:

x - the initial root approximation.

Returns:

a root that lies close to x.

Throws:

NumericException - if a root could not be found.

getDerivative

public Function getDerivative()

Access the derivative of the target function.

Returns:

the target function derivative.

getFunction

public Function getFunction()

Access the target function.

Returns:

the target function.

setDerivative

public void setDerivative(Function f)

Modify the derivative of the target function.

Parameters:

f - the new target function derivative.

setFunction

public void setFunction(Function f)

Modify the target function.

Parameters:

f - the new target function.