fixed point

package fixedpoint;

import java.util.Scanner;

public class FIXEDPOINT
{
    static double E = 0.001;

    public static double F(double x)
    {
        double result = Math.pow(x, 3) - x - 1 ; // x3-x-1=0
        return result;
    }

    public static double G1(double x)
    {
        double result = Math.pow(x,3)-1 ; // x3-1
        return result;
    }

    public static double G2(double x)
    {
        double result = Math.pow((x+1),1/3) ; // (x+1)^(1/3)
        return result;
    }

    public static double G3(double x)
    {
        double result = 1/(Math.pow(x,2)-1) ; // 1/(x2-1)
        return result;
    }

    public static double dG1(double x)
    {
        double result = 3*Math.pow(x,2); //3x2
        return result;
    }

    public static double dG2(double x)
    {
        double result = 1/(3*Math.pow((x+1),2/3)); //  1/(3*(x+1)^(2/3))
        return result;
    }

    public static double dG3(double x)
    {
        double result = (-2*x)/(Math.pow(Math.pow(x,2)-1,2)); // -2x/(x2-1)^2
        return result;
    }

    public static int convergence(double x)
    {
        if(dG1(x)<1)
        {
            return 1;
        }
        else if(dG2(x)<1)
        {
            return 2;
        }
        else if(dG3(x)<1)
        {
            return 3;
        }
        return 0;
    }

    public static void main(String[] args)
    {
        System.out.println("Enter initial guess : ");
        Scanner scanner = new Scanner(System.in);
        double root = scanner.nextDouble();
        double update ;
        int iteration = 1;
        //determine which conversion will go
        int choice = convergence(root);
        if(choice==1)
        {
            while(true)
            {
                update = G1(root);
                if(Math.abs(update-root)<E)
                {
                    break;
                }
                System.out.println("Iteration : "+iteration+" X = "+update);
                iteration++;
                root=update;
            }
        }
        else if(choice==2)
        {
            while(true)
            {
                update = G2(root);
                if(Math.abs(update-root)<E)
                {
                    break;
                }
                System.out.println("Iteration : "+iteration+" X = "+update);
                iteration++;
                root=update;
            }
        }
        else if(choice==3)
        {
            while(true)
            {
                update = G3(root);
                if(Math.abs(update-root)<E)
                {
                    break;
                }
                System.out.println("Iteration : "+iteration+" X = "+update);
                iteration++;
                root=update;
            }
        }
        else
        {
            System.out.println("");
        }
        System.out.println("The root is "+root+" after "+iteration+" iterations");
    }

}