% code for fitting cubic spline with Matlab's default not-a-knot end
% condition to the famous Runge function 1/(1+x^2)
clear;
a=-5;b=5;n=10;
xknots = linspace(a,b,n+1);
yknots = 1./(1+xknots.^2);

% calculate the spline; information in pp
pp=spline(xknots,yknots);

% now evaluate it on a fine grid;
neval=100;
xeval = linspace(a,b,neval);
yeval=ppval(pp,xeval);

% plot it, showing knots
figure(1);
plot(xknots,yknots,'o',xeval,yeval,'-');
xlabel('x'); ylabel('f');
title('Cubic spline for 1/(1+x^2) with n=10');