5.2 Java Code for Newton's Method

class Newton  {

    static double f(double x) {
	return Math.sin(x);
    }

    static double fprime(double x) {
        return Math.cos(x);
    }

    public static void main(String argv[]) {

	  double tolerance = .000000001; // Our approximation of zero
	  int max_count = 200; // Maximum number of Newton's method iterations

/* x is our current guess. If no command line guess is given, 
   we take 0 as our starting point. */

	  double x = 0;

	  if(argv.length==1) {
	    x= Double.valueOf(argv[0]).doubleValue();
	  }

         for( int count=1;
                  (Math.abs(f(x)) > tolerance) && ( count < max_count);
                 count ++)  {
            x= x - f(x)/fprime(x);
	    System.out.println("Step: "+count+" x:"+x+" Value:"+f(x));
	  }            

	  if( Math.abs(f(x)) <= tolerance) {
	   System.out.println("Zero found at x="+x);
	  }
	  else {
	   System.out.println("Failed to find a zero");
	  }
     }

}

5.3 Compiling and Running the Newton Class

David Maxwell, who is still writing this, would like to hear your comments and suggestions.