clear
format long
format compact

%%
% We set up a 5x5 triangular matrix with prescribed eigenvalues on
% its diagonal.
lambda = [1 -0.75 0.6 -0.4 0];
A = triu(ones(5),1) + diag(lambda); 

%%
% We run RQ iteration with the initial shift s=0.7 and take the final
% estimate as our ``exact'' answer to observe the convergence. 
[gamma, m, x] = rqiter(A, 0.7, 10);
eigval = gamma(m)
m

%%
% As expected, the eigenvalue that was found is the one closest to 0.7.
err = eigval - gamma;
semilogy(abs(err(1:m)),'.-')
title('Convergence of inverse iteration')
xlabel('k')
ylabel('|\lambda_1 - \gamma_k|')
grid on