newpoly(X,Y)

function [C,D] = newpoly(X,Y)
%---------------------------------------------------------------------------
%NEWPOLY   Construction of the collocation polynomial.
%          The method is Newton interpolation.
% Sample calls
%   [C] = newpoly(X,Y)
%   [C,D] = lnewpoly(X,Y)
% Inputs
%   X   vector of abscissas
%   Y   vector of ordinates
% Return
%   C   coefficient list for the Newton polynomial
%   D   divided difference table
%
% 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 4.5 (Newton Interpolation Polynomial).
% Section	4.4, Newton Polynomials, Page 234
%---------------------------------------------------------------------------

n = length(X);
D = zeros(n,n);
D(:,1) = Y';
for j=2:n,
  for k=j:n,
      D(k,j) = (D(k,j-1)-D(k-1,j-1))/(X(k)-X(k-j+1));
  end
end
C = D(n,n);
for k=(n-1):-1:1,
  C = conv(C,poly(X(k)));
  m = length(C);
  C(m) = C(m) + D(k,k);
end