Extensions of Perron-Frobenius splittings and relationships with nonnegative Moore-Penrose inverses

An -matrix has the form , where and is eventually nonnegative, i.e. is entry wise nonnegative for all sufficiently large integers . In this article, two new types of splittings of matrices are introduced. The class of matrices possessing a splitting of one of these types includes -matrices as a subclass. The authors derived necessary and sufficient conditions for the convergence of these splittings in terms of an extended notion of the nonnegativity of the Moore-Penrose inverse. The work reported here widens the applicability of the existing results.