clear
format compact

%%
% The following experiments are based on a matrix resulting from
% discretization of a partial differential equation.
maxit = 120;  
rtol = 1e-8;
d = 50;
A = d^2*gallery('poisson', d);
n = size(A, 1)
b = ones(n, 1);

%%
% We compare unrestarted GMRES with three different thresholds for
% restarting.
rest = [120 20 40 60]; 
for j = 1:length(rest)
    [~,~,~,~,rv] = gmres(A, b, rest(j), rtol, maxit/rest(j));
    semilogy(0:length(rv)-1, rv, '-')
    hold on;    
end
title('Convergence of restarted GMRES')
xlabel('m')
ylabel('residual norm')
legend('no restart','every 20','every 40','every 60','location','southwest')
grid on

%%
% The ``pure'' curve is the lowest one. All of the other curves agree with
% it until they encounter their first restart.