newton raphson method in java ?? does it exist

SUNIL GUTTA

13y5.4kJava

actually its my friends assignment to do this thing .. he asked me i am shell shocked . i never heard about it .. any suggestions offered .

He wanted to do x^3-x+1 using newton raphson in java ???

Cheers

3 Replies

Know the answer? Post it — somebody with the same question will find it here.

Vulpes13y ago
Accepted answer
There isn't anything built into the Java standard library to my knowledge, but try this:

// Polynomial.java

import java.io.*;

public class Polynomial
{
int degree;

double[] terms;

public Polynomial(double[] terms)
{
this.terms = terms;
this.degree = terms.length - 1;
}

public Polynomial differentiate()
{
if (degree == 0) return new Polynomial(new double[] { 0.0 });
double[] deriv = new double[degree];
int deg = degree;
int len = terms.length;

for (int i = 0; i < len - 1; i++)
{
deriv[i] = (deg--) * terms[i];
}

return new Polynomial(deriv);
}

public double evaluate(double x)
{
double val = 0;
int len = terms.length;
double pow = 1;

for (int i = len - 1; i >= 0; i--)
{
if (terms[i] != 0)
{
val += terms[i] * pow;
}
pow *= x;
}

return val;
}

public double solve (double guess)
{
Polynomial deriv = this.differentiate();
double x0 = guess;
double x1 = x0;
double diff;
Boolean convergent = true;
int count = 0;

do
{
double divisor = deriv.evaluate(x0);
if (divisor == 0)
{
convergent = false;
break;
}
x1 = x0 - this.evaluate(x0)/divisor;
diff = Math.abs(x1 - x0);
x0 = x1;
count++;
}
while (diff > 0.00000001 && count < 100);

if (!convergent || count == 100)
{
System.out.println("May be non-convergent. Stopped after " + count + " iterations");
}

return x1;
}

}

// Newton.java

import java.io.*;

class Newton
{
public static void main(String[] args) throws IOException
{
double[] terms = {1, 0, -1, 1}; // x^3 - x + 1
Polynomial p = new Polynomial(terms);
double result = p.solve(1);
System.out.println("The method gives a root of " + result);
System.out.println("The residue for this root is " + p.evaluate(result));
}
}

The output should be:

The method gives a root of -1.324717957244746
The residue for this root is 0.0
Vulpes13y ago
Newton-Raphson is a method for finding a root of a function (i.e. a value of x for which f(x) = 0) by successive approximation. You start with a guess (x0) at what the root should be and then refine your guess using the formula:

x1 = x0 - f(x0)/f'(x0);

You then set x0 = x1 and work out a new value for x1 and keep on going like this until (hopefully) the results converge towards an answer.

Sometimes the results won't converge if the initial guess is poor or for other reasons.

Although formulas exist for finding the roots of cubic and quartic equations (but not for polynomials of higher degree) these are very cumbersome to use and so approximate methods such as Newton-Raphson may be preferred in practice.

If you examine my Polynomial.solve() method, you'll see that I'm using Newton-Raphson to find a root of the polynomial to a high degree of accuracy.
SUNIL GUTTA13y ago
Hi

Well i am very much more into c# as you also know :)

In this doubt of my friend you answered with ease . how ? Did u work with this some so called newton raphson method ??

i want to know What is the use of this method :)

cheers