We measure the convergence rate for piecewise linear interpolation of .

f = @(x) exp(sin(7*x));

x = linspace(0,1,10001)'; % sample the difference at many points

n_ = 2.^(3:10)';

err_ = 0*n_;

for i = 1:length(n_)

n = n_(i);

t = linspace(0,1,n+1)'; % interpolation nodes

p = plinterp(t,f(t));

err = max(abs( f(x) - p(x) ));

err_(i) = err;

end

Since we expect convergence that is , we use a log-log graph of error and expect a straight line of slope .

loglog( n_, err_, '.-' )

hold on, loglog( n_, 0.1*(n_/n_(1)).^(-2), '--' )

xlabel('n'), ylabel('||f-p||_\infty') % ignore this line

title('Convergence of PL interpolation') % ignore this line

legend('error','2nd order') % ignore this line

axis tight % ignore this line