# -*- coding: utf-8 -*-
"""
Created on Mon Aug 26 21:52:16 2013

This is homework0.py. It uses python to calculate sqrt(2) by solving 
x^2 = 2. We use the method detailed in class ( successive approximation). 
We solve x = f(x) where f(x) = (x + 2/x)/2. 

Start with x0 = 1.0. change initial values of x and see what happens. You
may have to change the number of iterations also 

@author: dave semeraro
"""
from math import sqrt;
x=1.0;
gx = 0.0;
numberofiterations = 5;
for i in range(numberofiterations):
    gx = (x + 2.0/x)/2.0;
    x = gx;
    err = sqrt(2.0) - gx;
    relerr = err/sqrt(2.0);
    print '%3d %13e %13e' % (i, err, relerr);