We present an extension to the subgradient algorithm to produce primal as w
ell as dual solutions. It can he seen as a fast way to carry out an approxi
mation of Dantzig-Wolfe decomposition. This gives a Fast method for produci
ng approximations for large scale linear programs. It is based on a new the
orem in linear programming duality. We present successful experience with l
inear programs coming from set partitioning, set covering, max-cut and plan
t location.