%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----

close all; clc; clear; 

% Problem EPage 118 
% 
for n=[ 200, 400, 600, 800, 1000, 1200, 1400 ] , 
  
  h = 2/n;

  A = diag( -2/h^2 * ones(1,n) );
  A = A + diag( 1/h^2 * ones(1,n-1), 1 );
  A = A + diag( 1/h^2 * ones(1,n-1), -1 );
  A = -A;

  [V,D] = eig(A);

  % we want the smallest eigenvalue: 
  % 
  disp( sprintf( 'n= %5d approximate ev= %10.6f, true ev= %10.6f\n', n, min( diag(D) ), (pi/2)^2 ) );

end