function Apr25()
% Substitute Jc = USV' into (Jc'*Jc + lambda*I)*sc = -Jc'*Fc
% Get
%          V*(S'*S + lambda*I)V'*sc = -V*S'*(U'*Fc)
% so if b = U'*Fc, stilde = V'*sc,  and S = diag(sig(1),...,sig(n)), we have
%
%   ( diag(sig(1)^2,...,sig(n)^2) + lambda*I )*stilde = -S'*b
%
% Thus, stilde(i) = -sig(i)*b(i)/(sig(i)^2 + lambda),   i=1:n
%
% Since stilde = V'sc, norm(stilde) = norm(s). So we give fzero this
% function:
%      f(lambda) = sum_{i=1}^{n} (sig(i)*b(i)/(sig(i)^2 + lambda))^2 - mu^2
%
% where mu is the desired norm of the solution .