% code for fitting polynomials to the famous Runge function 1/(1+x^2)
clear;
a=-5;b=5;n=10;
piapprox=3.141592654;

% calculate Chebyshev points
inx=0:n;
xknots=0.5*(a+b)+0.5*(b-a)*cos((2*inx+1)*piapprox/(2*n+2));
yknots = 1./(1+xknots.^2);
p=polyfit(xknots,yknots,n);

neval=100;
xeval = linspace(a,b,neval);
yeval=polyval(p,xeval);

figure(2);
plot(xknots,yknots,'o',xeval,yeval,'-');
xlabel('x'); ylabel('f');
title('Polynomial interpolant for 1/(1+x^2) with n=10, Chebyshev');