/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
	 by RH Landau, MJ Paez, and CC Bordeianu 
	 Copyright Wiley-VCH, 2007.
	 Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
	 MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
	 Support by National Science Foundation															 
*/
// Newton_cd.java: Newton-Raphson root finder, central diff deriv

public class Newton_cd	{

	public static double f(double x)			// Find zero of this function
	 { return 2*Math.cos(x) - x; }
	 
	public static void main(String[] argv) {	
		
		double x = 2., dx = 1e-2, F= f(x), eps = 1e-6, df;	 
		int it, imax = 100;						  // Max no of iterations permitted
		                                                       // Iterate
		for ( it = 0;	 it <= imax;	it++ )	{			
			System.out.println("Iteration # = "+it+" x = "+x+" f(x) = "+F);
			                                          // Central diff deriv
			df = ( f(x + dx/2) - f(x-dx/2) )/dx;					
			dx = -F/df; 
			x += dx;																					 // New guess
			F = f(x);																				// Save for use
			                                       // Check for convergence
			if ( Math.abs(F) <= eps )	 {							 
				 System.out.println("Root found, tolerance eps = " + eps); 
				 break; 
} } } }