  function Mar7()
% M = inv(G)*(A + u*u')inv(G') = I + v*v'  where 
v = G\u;
% Using Sherman-Morrison, inv(M) = I - mu*v*v' where
mu = 1/(1+v'*v);
% here is an O(n^2) method for the required condition...
I = eye(n,n);
condOfM = norm(I+v*v',1)*norm(I-mu*v*v');
% It is possible to compute the 1-norm of I-plus-rank1 in O(n) flops.
condOfMBetter = SpecialOneNorm(1,v)*SpecialOneNorm(-mu,v);

% However, since G\u is O(n^2), this cool fact doesn't real change the overall
% O(n^2) complexity

  function tau = SpecialOneNorm(mu,v)
% v is a column n-vector and mu is a scalar. 
% tau = norm(eye(n,n)+mu*v*v);
tau = 0;
n = length(v);
w = mu*v;
beta = norm(w,1);
for k=1:n
    % Note that the kth column of eye(n,n)+ w*v' is 
    %          ek+v(k)*w  where ek = I(:,k)
    % The one norm of this vector is
    OneNormCol_k = beta*abs(v(k)) - abs(w(k)*v(k)) + abs(1+w(k)*v(k));
    tau = max(tau,OneNormCol_k);
end