% Script: qriter_test.m
% Exapmle script for QR iteration to find eigenvalues
%

close all; clear all;
n = 10;
D = diag((1:n)');
V = randn(n);   % Interesting results if orthogonal matrix here instead!
Ak = V*D/V;

maxiter = 20;
approx = [];
for k=1:maxiter
    [Q,R] = qr(Ak); Ak = R*Q; approx = [approx Ak(n,n)];
end
format long
disp('The approximation to the smallest eigenvalue:')
approx'
plot(log(abs(approx)));
xlabel('k'); ylabel('smallest eigenvalue'); 

% now look at error behavior
err = abs( approx-1 );
figure
plot(log(err));
xlabel('k'); ylabel('error in smallest eigenvalue');
format short e
disp('The error in the smallest eigenvalue:')
err'