close all; clc; clear; 

a_value = 2;
b_value = 1; 

% Problem EPage 45
% 
for n=20:10:50
  b = ones( n,1 ); 
  
  A_full = diag( a_value*ones(1,n) ) + diag( b_value*ones(1,n-1), +1 ) + diag( b_value*ones(1,n-1), -1 );
  
  rowpos = [ 1:n, 1:(n-1), 2:n ];
  colpos = [ 1:n, 2:n, 1:(n-1) ];
  values = [ a_value*ones(1,n), b_value*ones(1,n-1), b_value*ones(1,n-1) ];
  A_sparse = sparse( rowpos, colpos, values, n, n );
  
  tic; A_full \ b; t_full = toc;
  tic; A_sparse \ b; t_sparse = toc;
  
  disp( sprintf('n= %5d, time full= %10.6f, time sparse= %10.6f', n, t_full, t_sparse) );
end