cheby(f,n,a,b)

function [C,X,Y] = cheby(f,n,a,b)
%---------------------------------------------------------------------------
%CHEBY   Construction of the collocation polynomial.
%        The method is Chebyshev interpolation.
% Sample calls
%   [C] = cheby('f',n)
%   [C,X,Y] = cheby('f',n)
%   [C,X,Y] = cheby('f',n,a,b)
% Inputs
%   f   name of the function 
%   n   degree of the Chebyshev interpolation polynomial
%   a   left  endpoint of the interval
%   b   right endpoint of the interval
% Return
%   C   coefficient list for the Chebyshev interpolation polynomial
%   X   abscissas for interpolation nodes
%   Y   ordinates for interpolation nodes
%
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1995
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% Prentice Hall, Inc.; USA, Canada, Mexico ISBN 0-13-624990-6
% Prentice Hall, International Editions:   ISBN 0-13-625047-5
% This free software is compliments of the author.
% E-mail address:      in%"[e-mail]"
%
% Algorithm 4.6 (Chebyshev Approximation).
% Section	4.5, Chebyshev Polynomials, Page 246
%---------------------------------------------------------------------------

if nargin==2, a=-1; b=1; end
d = pi/(2*n+2);
C = zeros(1,n+1);
for k=1:n+1,
  X(k) = cos((2*k-1)*d);
end
X = (b-a)*X/2+(a+b)/2;
x = X;
Y = eval(f);
for k = 1:n+1,
  z = (2*k-1)*d;
  for j = 1:n+1,
    C(j) = C(j) + Y(k)*cos((j-1)*z);
  end
end
C = 2*C/(n+1);
C(1) = C(1)/2;