function plot_omega( n )
%function plot_omega( n )
%
% Matlab function to plot the term from the Chebyshev minimax problem:
%
%     | omega(t) | = | (t-t[0]) * ... * (t-t[n]) |
%
% for equi-spaced vs Chebyshev vs modified Chebyshev nodes on [-1,1]
% for the input value of 'n'.
%
% C.G. (11-96)
%

m = 1000 ;  t = [ 0 : m ]' * 2 / m - 1 ;       % number/vector of sample points

%
% 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 3 |omega(t)| functions on the sample points.
%

omega = zeros( m + 1, 3 ) ;      % initialize an array of the proper dimensions

for k = 1 : 3
   omega(:,k) = abs( polyval( poly( tau(:,k) ), t ) ) ;
end

clf ,  plot( t, omega )

title( [ 'Chebyshev vs Equally Spaced,  ', '|\omega({\it{x}})|,  ', ...
         '{\it{n}} = ', num2str(n) ] )

xlabel('{\it x}') ,  ylabel('{\it y}')