% 4-7-2008
% Jacobi's Method

clear all;
close all;

% Settings
TOLERANCE = 10^(-6);
max_iterations = 1000;

% Initial guess
x(1)=1;
y(1)=2;
z(1)=2;

for i=2:max_iterations
    % Convergent iteration scheme
    x(i) = (7 + y(i-1) - z(i-1))/4;
    y(i) = (21 + 4*x(i-1) + z(i-1))/8;
    z(i) = (15 + 2 * x(i-1) - y(i-1)) / 5;
    
    % Check to see if we have converged, look up 'help norm' to find out
    % what it does.
    if ( norm([x(i) y(i) z(i)]-[x(i-1) y(i-1) z(i-1)],2) < TOLERANCE )
        break;
    end
end

% Plot convergence
plot(x,'o-')
hold on
plot(y,'ro-')
plot(z,'ko-')
axis([1 i 0 4.1])
legend('x','y','z')
title('Convergence of Jacobi Method')
xlabel('Iteration');
ylabel('Value of (x y z)');