An improved Newton iteration for the weighted Moore-Penrose inverse

In this paper, we showed that Newton iteration may be used to compute the weighted Moore-Penrose inverse of an arbitrary matrix. We also take advantage of several new acceleration procedures to reduce the cost of Newton iteration, which extends the earlier work [R. Schreiber, Computing generalized inverses and eigenvalues of symmetric matrices using systolic arrays, in: R. Glowinski, J.L. Lious (Eds.), Computing Methods in Applied Science and Engineering, North-Holland, Amsterdam, 1984; T. Söderstörm, G.W. Stewant, On the numerical properties of an iterative method for computing the Moore-Penrose generalized inverse, SIAM J. Numer. Anal. 11 (1974) 61-74].