function demo2
%  *** Illustration of Assignment4, Problem 3 ***
   close all
   format compact
   set(0,'DefaultAxesFontSize',15)
   set(0,'DefaultAxesLinewidth',1) 
   for n=round(logspace(1,8,100))
     x=linspace(0,1,n+2)';
     x=x(2:n+1);
%    *** Sparse system matrix ***
     A=spdiags([ones(n,1),-2*ones(n,1),ones(n,1)],-1:1,n,n);    
%    *** Right hand side and reference solution ***
     rhs=2*(6*x.^2-1);  
     yref=(n+1)^2*(x.^2.*(x-1).*(x+1));
%
%    *** Matlab backslash ***   
     y=A\rhs;
     myerr1=norm(y-yref)/norm(yref);
%
%    *** Solution based on matrix-vector multiplication with inverse ***
     k=[1:n]';
     y=flipud(cumsum(k.*flipud(rhs)));
     y=-(flipud(k).*cumsum(k.*rhs)+k.*[y(2:n);0])/(n+1);
     myerr2=norm(y-yref)/norm(yref);
%
     condA=(1+cos(pi/(n+1)))/(1-cos(pi/(n+1)))
     loglog(n,myerr1,'*',n,myerr2,'o',n,eps*condA,'d')
     title('Convergence with n')
     ylabel('Relative Error ||y-y_tilde||/||y||')
     xlabel('Number of points n')
     hl=legend('Backslash','Accurate inverse','eps*cond(A)','Location','North');
     set(hl,'Fontsize',14)
     hold on
     grid on
     drawnow
   end