M-Matrices Leading to Semiconvergent Splittings.

摘要

An M-matrix as defined by Ostrowski is a matrix that can be split into A=sI-B, s > 0, B > or = 0 with s > or = rho (B), the spectral radius of B. M-matrices with the property that the powers of T=(1/s)B converge for some s are studied and are characterized here in terms of the nonnegativity of the group generalized inverse of A on the range space of A, extending the well-known property that 1/A > or = 0 whenever A is nonsingular. (Author)