function polycos(m,n);
% Polynomial least squares fit of cos(4t).  See Tref & Bau exercise 11.3.
% Calling:     polycos(m,n) for m points and degree n-1 polynomial fit.
% Depends on:  mgs2 and house.m

t=linspace(0,1,m);  A=fliplr(vander(t));  A=A(:,1:n);  b=cos(4*t');
xa=(A'*A)\(A'*b);
[Q R]=mgs2(A); xb=R\(Q'*b);
[Q R]=house(A); xc=R\(Q'*b);
[Q R]=qr(A,0); xd=R\(Q'*b);
xe=A\b;
[U S V]=svd(A,0); xf=V*(S\(U'*b));
format long, disp([xa xb xc xd xe xf]')