// ROOT FINDING
// Program 4 : To impliment Iteration Method

#include <stdio.h>
#include <conio.h>
#include <math.h>

#define  F(x) ( x*x*x - 2*x + 1 )
#define  G(x) ( ( x*x*x + 1 ) / 2 )

#define EPS 0.00005

main()
{
	int i, n;
	float x0, x1, e;
	
	printf("\n Enter initial approx. root (x0) : ");
	scanf("%f", &x0);
	
	printf("\n Enter the no of max iterations : ");
  	scanf("%d", &n);
	
	for( i=1; i<=n ; i++)
   	{
		x1 = G(x0);
		
		printf("\n Iter. %d \t\t Xn = %f \t\t Xn+1 = %f", i, x0, x1);
		
		e = fabs( (x1 - x0) / x1 );
		
		if( e < EPS )
			break;
		
		x0 = x1;
   	}
   	
  	if( e <= EPS )
   		printf("\n\n Root = %f", x1);
   	else
  		printf("\n\n INSUFFICIENT ITERATIONS ");
  	
  	getch();
}