% plots showing rate of convergence.
%
% NOTE: if you want to use plots like these in your lab, you 
% need to explain how they demonstrate rate of convergence.

% plot 1

g = inline('sqrt(1+x)');
x = fixed(g, 1, 1e-10, 100);
err = log(abs(x - (1 + sqrt(5))/2));

subplot(2,1,1)
plot(err, 'ro-');

xlabel('n');
ylabel('log|x_n - \alpha|');
title('linear convergence of x_{n+1} = sqrt(1 + x_n) with x_0 = 1');

% plot 2

g = inline('x/2 + 1/x');
x = fixed(g, 1, 1e-10, 100);
err = log(abs(x - sqrt(2)));

subplot(2,1,2);
k = length(err);
plot(2.^(1:k), err, 'ro-');

xlabel('2^n');
ylabel('log | x_n - \alpha |');
title('quadratic convergence of x_{n+1} = x_n/2 + 1/x_n with x_0 = 1');