%
% Matlab script file to illustrate some features of polynomial
% interpolation: Lebesgue constants, Chebyshev abscissae vs
% equi-distant nodes, etc.
%
% C.G. (11-96)
%

m = 800 ;  t = [ 0 : m ]' * 2 / m - 1 ;        % number/vector of sample points

%
% Loop over n = 5, 10, 15, 20.
%

for in = 1 : 4

  n = 5 * in ;
%
% put the different node sets in the columns of the array tau.
%
  tau = zeros( n + 1, 3 ) ;      % initialize an array of the proper dimensions

  tau(:,1) = [ 0 : n ]' * 2 / n - 1 ;          % equally spaced nodes on [-1,1]
  tau(:,2) = - cos( ( 2*[0:n]' +  1 ) * pi / ( 2*n + 2 ) ) ;  % Chebyshev nodes
  tau(:,3) = - cos( [ 0 : n ]' * pi / n ) ;          % modified Chebyshev nodes
%
% evaluate the Lebesgue constant for these three node sets on [-1,1].
%
  imask = ones( n+1, 1 ) ;  ident = eye( n+1 ) ;   % init mask and unit vectors

  for k = 1 : 3

    sum = zeros( m+1, 1 ) ;          % initialize sum (at each t point) to zero

    for i = 0 : n
      p   = poly( tau(logical(imask-ident(:,i+1)),k) ) ; % coeff's of i'th
                                                         % Lagrange poly
      sum = sum + abs( polyval( p, t ) / polyval( p, tau(i+1,k) ) ) ;
    end

    table(in,k+1) = max( sum ) ;

  end

  table(in,1) = n ;

end

table