%% Demonstrate rates of convergence % In this demo, we'll see linear, superlinear, quadratic, cubic, and % arithmetically convergence to zero. %% Setup the plot clf; cla; hold on; k=(1:60)'; xlim([0,60]); ylim([1e-8,1]); %% Start with linear seq = 0.85.^k semilogy(k, seq, 'k-', 'LineWidth', 2); text(max(k), seq(end), 'Linear', 'FontSize', 20); % Fix small bug in matlab set(gca,'YScale','log'); %% Arithmetic semilogy(k, 1./k, ':', 'Color', [0,0.8,0], 'LineWidth', 2); seq = 1./(k.^2) semilogy(k, seq, ':', 'Color', [0,0.8,0], 'LineWidth', 2); text(max(k), seq(end), 'Arithmetic', 'FontSize', 20); %% Superlinear seq = (2*k).^(-0.05*k) semilogy(k, seq, '-.', 'Color', [0.8,0,0], 'LineWidth', 2); text(max(k), seq(end), 'Superlinear', 'FontSize', 20); %% Quadratic seq = (0.99).^(2.^k) semilogy(k, seq, '--', 'Color', 'm', 'LineWidth', 2); text(12, 5e-8, 'Quadratic', 'FontSize', 20); %% Cubic seq = (0.99).^(3.^k) semilogy(k, seq, '--', 'Color', 'y', 'LineWidth', 2); text(5, 5e-8, 'Cubic', 'FontSize', 20, 'HorizontalAlignment','right');