You could just overlay the respective curve-fit to your plot.
K_tilde_linear = M^(-1/2).*K.*M^(-1/2);
f=fit((1:14)',diag(K_tilde_linear),'poly1');
figure;
plot(f,(1:14)',diag(K_tilde_linear));
K_tilde_quad = M^(-1/2).*K_quadratic.*M^(-1/2);
f=fit((1:14)',diag(K_tilde_quad),'poly2');
figure;
plot(f,(1:14)',diag(K_tilde_quad));
K_tilde_expo_5 = M^(-1/2).*K_expo_5.*M^(-1/2);
f = fit((1:14)',diag(K_tilde_expo_5),'exp2');
figure;
plot(f,(1:14)',diag(K_tilde_expo_5));
K_tilde_expo_10 = M^(-1/2).*K_expo_10.*M^(-1/2)
f = fit((1:14)',diag(K_tilde_expo_10),'exp2');
figure;
plot(f,(1:14)',diag(K_tilde_expo_10));
