% Script: Ordofconv
% two sequences illustrating linear and quadratic convergence
%
x=1:50; y1 = 2.^-(x-1);
x2 = 1:10; y2 = 2.^(-2.^(x2-1));
figure(1)  % open first figure
semilogy(x,y1,'-',x2,y2,'--') % semilog plot for showing decay with n
xlabel('n')
legend('a_n: linear','b_n: quadratic',4)
title('Decay of a_n and b_n with n')
pause
%
% now illustrate rate of convergence
figure(2)   % open secone figure, keeps first
loglog(y1(1:end-1),y1(2:end),'-',y2(1:end-1),y2(2:end),'--')
xlabel('a_n')
ylabel('a_{n+1}')
legend('a_n: linear','b_n: quadratic',4)
title('Rate of Convergence')