% BADINTERP  Script to show bad result from equally-spaced interpolation of
% f(x)=1/(1+x^2).
% ELB 5/2/05
% See also: GOODINTERP

% choose N and distribute points
N=40;
x=linspace(-12,12,N+1);  % equally-spaced

% fit degree N polynomial to  1/(1+x^2)
f=inline('1./(1+x.^2)','x');
y=f(x);
% following command reports warning if N > 9 because we unnecessarily 
% convert to monomial basis:
p=polyfit(x,y,N);

% plot the result
xx=-12:0.01:12;
yy=polyval(p,xx);
plot(x,y,'o',xx,yy), axis([-12 12 -1 2])