An improved method for the computation of the Moore-Penrose inverse   matrix
  In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better accuracy than the already proposed methods, while works for full and sparse matrices. 
Vasilios N. Katsikis, Dimitrios Pappas, Athanassios Petralias
math.NA