function main();

// Main function for iteration of static values in 
// eigenvalue problem
//
//
// Grundlagen der Modellierung und Simulation
// WiSe 2012/13


//%%%%%%%%%%%%%%%%%%%%%% Start Values %%%%%%%%%%%%%%%%%%%%

x = [-3; 0; 0]

//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

x_fixpunkt = x;
x_newton = x;
x_qnewton = x;

//%%%%%%%%%%%%%%%%%%% Fixpunkt %%%%%%%%%%%%%%%%%%%%%%%%%%%

[it_f, x_f] = fixpoint(x_fixpunkt);

//%%%%%%%%%%%%%%%%%%% Newton %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[it_n, x_n] = newton(x_newton);

//%%%%%%%%%%%%%%%%%%% Quasi-Newton %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[it_qn, x_qn] = quasi_newton(x_qnewton);


//%%%%%%%%%%%%%%%%%%% Output %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp('Startwert x');
x

disp('Anzahl Iterationen bei Fixpunkt:');
it_f
disp('Loesung:');
x_f(:,it_f)
%x_f

disp('Anzahl Iterationen bei Newton:');
it_n
disp('Loesung:');
x_n(:,it_n)
%x_n
disp('Anzahl Iterationen bei Quasi-Newton:');
it_qn
disp('Loesung:');
x_qn(:,it_qn)


semilogy(1:it_n, abs(x_n(3,:)-2), ...
    1:it_f, abs(x_f(3,:)-2), ...
    1:it_qn, abs(x_qn(3,:)-2)) 
title('Iterationsverfahren');
legend('error (Newton) ','error (FixP)','error (Quasi-Newton)')
xlabel('Anzahl Iterationen');
ylabel('Fehler in lambda');

endfunction