%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
% Problem on EPage 62; Solutions on EPage 161
%
%-----

close all; clc; clear all; 

addpath('../../BookCode');

a = 100.112;
tol = 1.e-6;

% First iteration method: 
%
xk = 1000;
xkp1 = (xk + a/xk)/2;
it = 1;
x_iters = [xk,xkp1];
d = abs(xkp1 - xk);
while d > tol ,
  xk = xkp1;
  xkp1 = (xk + a/xk)/2;
  d = abs(xkp1 - xk);
  x_iters = [ x_iters, xkp1 ];
end

ph1 = plot( x_iters, '.-r' );
grid('on'); hold('on');
ph_truth = plot( sqrt(a)*ones( 1, length(x_iters) ), '-g' );

% Second iteration method: 
%
xk = 1000;
xkp1 = (xk + a/xk)/2 - (xk - a/xk)^2 / (8*xk);
it = 1;
x_iters = [xk,xkp1];
d = abs(xkp1 - xk);
while d > tol ,
  xk = xkp1;
  xkp1 = (xk + a/xk)/2 - (xk - a/xk)^2 / (8*xk);
  d = abs(xkp1 - xk);
  x_iters = [ x_iters, xkp1 ];
end

ph2 = plot( x_iters, '.-b' );

legend( [ph1,ph2,ph_truth], {'iterates method 1', 'iterates method 2','truth'} );

%saveas( gcf, '../../WriteUp/Graphics/Chapter3/c_3_p_17_plot.eps', 'epsc' );