% code for fitting polynomials 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);
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, equally spaced');