close all; clc; clear; 

% Problem EPage 46
% 
n = 20
E = c_2_p_10_mk_E(n);
[approx_V,approx_D] = eig(E);
approx_D = sort( diag( approx_D ) ); 
ks = ( 1:n ).';
exact_D = sort( 1 ./ ( 2 - 2 * cos( ks * pi / (n+1) ) ) );
norm( approx_D - exact_D )

n = 50
E = c_2_p_10_mk_E(n);
[approx_V,approx_D] = eig(E);
approx_D = sort( diag( approx_D ) ); 
ks = ( 1:n ).';
exact_D = sort( 1 ./ ( 2 - 2 * cos( ks * pi / (n+1) ) ) );
norm( approx_D - exact_D )