An improved Newton iteration for the weighted Moore–Penrose inverse

摘要

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].