Newtons Method of Finding Square Root
```/*************************************************************************
*
* Last updated: Wed Oct 3 09:44:15 EDT 2007.
*  Compilation:  javac Newton.java
*  Execution:    java Newton x0 x1 x2 x3
*
*  Compute the square root using Newton's method. Package it
*  in a static method.
*
*  % java Newton 1 2 3 1000000.1 -2 0 -0 NaN Infinity -Infinity
*  1.0
*  1.414213562373095
*  1.7320508075688772
*  1000.0000499999987
*  NaN
*  0.0
*  -0.0
*  NaN
*  Infinity
*  NaN
*
*************************************************************************/

public class Newton {

// return the square root of c, computed using Newton's method
public static double sqrt(double c) {
if (c < 0) return Double.NaN;
double EPS = 1E-15;
double t = c;
while (Math.abs(t - c/t) > EPS*t)
t = (c/t + t) / 2.0;
return t;
}

// overloaded version in which user specifies the error tolerance EPS
public static double sqrt(double c, double EPS) {
if (c < 0) return Double.NaN;
double t = c;
while (Math.abs(t - c/t) > EPS*t)
t = (c/t + t) / 2.0;
return t;
}

// test client
public static void main(String[] args) {

// parse command-line parameters
double[] a = new double[args.length];
for (int i = 0; i < args.length; i++) {
a[i] = Double.parseDouble(args[i]);
}

// compute square root for each command line parameter
for (int i = 0; i < a.length; i++) {
double x = sqrt(a[i]);
StdOut.println(x);
}
}
}
```
page revision: 1, last edited: 15 Jul 2008 20:04