Aitkens Process

///***************Solve a fixed quadratic equation using Aitken’s Delta-Squared Process***************///
///** a = 4; b = 6; c = -1 **///
///** Equation: 4x^2 + 6x - 1 = 0 **///
///** x1 = 0.151388 ; x2 = -1.65139 **///

#include<iostream>
#include<cmath>

#define ESP 0.000001


using namespace std;

int main()
{
    double x1, x2, x3, x4, y;

    //First Value

    cin >> x1 >> x2 >> x3;

    #define F(x) (x2-x1*x*x)/x3
    //#define F(x) (1-4*x*x)/6

    x1 = 1;                 //Initial Value
    for (int i=1; ; i=i+3)
    {
        x2 = F(x1);
        x3 = F(x2);

        if(fabs(x3-x2) < ESP)
        {
            cout << "First Value: " << x3 << endl;
            break;
        }

        else
        {
            y = x3-2*x2+x1;
            x1 = x3-(((x3-x2)*(x3-x2))/y);
        }
    }


    //Second Value

    //cin >> x1;

    x1 = 2;                 //Initial Value
    for (int i=1; ; i=i+3)
    {
        x2 = F(x1);
        x3 = F(x2);

        if(fabs(x3-x2) < ESP)
        {
            cout << "Second Value: " << x3 << endl;
            break;
        }

        else
        {
            y = x3-2*x2+x1;
            x1 = x3-(((x3-x2)*(x3-x2))/y);
        }
    }

    return 0;
}