On the convergence of splittings for a z-matrix

Abstract

In this paper, first we present a characterization of semiconvergence for nonnegative splittings of a singular Z-matrix, which generalizes the corresponding result of [1]. Second, a characterization of convergence for L1-regular splittings of a singular Z-matrix is given, which improve the result of [3]. Third, convergence of weak nonnegative splittings and regular splittings is discussed, and we obtain some necessary and sufficient conditions such that the splittings of a Z-matrix converge.