function badex2
  close all
  format compact
  m=input('Give system size: ');
  [V,R]=qr(randn(m));
  b=V(:,1);
  U=zeros(m);
  U(:,1:m-1)=V(:,2:m);
  U(:,m)=b;
  A=U*V';

  [X,D]=eig(A);
  condA=cond(A)
  condX=cond(X)
  x=A\b;
  xref=V(:,m);
  [xgmres,flag,relres,iter]=gmres(A,b,[],sqrt(m)*eps,m);
  GMRES_iterations=iter(2)
  relative_residual_backslash=norm(A*x-b)/norm(b)  
  relative_residual_GMRES=relres
  relative_error_x_backslash=norm(x-xref)/norm(xref)
  relative_error_x_GMRES=norm(xgmres-xref)/norm(xref)  
  
  figure(1)
  whitebg('b')
  plot(diag(D),'y*','MarkerSize',10)
  title('Spectrum of A')
  axis equal
  axis square
  axis([-1.1 1.1 -1.1 1.1])