clear
clc

%%
% Here are some points that we could consider to be observations of an
% unknown function on [-1,1].
n = 5;
t = linspace(-1,1,n+1)';  
y = t.^2 + t + 0.05*sin(20*t);
figure(1)
plot(t, y, '.')

%%
% The polynomial interpolant, as computed using polyfit, looks very
% sensible.
c = polyfit(t,y,n);     % polynomial coefficients
p = @(x) polyval(c,x);
grid on
hold on
fplot(p, [-1 1])

%%
% But now consider a different set of points generated in almost exactly
% the same way.
n = 18;
t = linspace(-1, 1, n+1)';  
y = t.^2 + t + 0.05*sin(20*t);
figure(2)
plot(t, y, '.')
grid on
 
%%
% The points themselves are unremarkable. But take a look at what happens
% to the polynomial interpolant.
c = polyfit(t, y, n);     % polynomial coefficients
p = @(x) polyval(c,x);
hold on
fplot(p, [-1 1])