Comparison results for K-nonnegative double splittings of K-monotone matrices

摘要

This paper introduces the K-nonnegative double splitting of a K-monotone matrix using knowledge of the matrices that leave a cone invariant. The convergence of this splitting is studied. Comparison theorems for two K-nonnegative double splittings of a K-monotone matrix are obtained. The results generalize the corresponding results introduced by Song and Song (Calcolo 48:245-260, 2011) for nonnegative double splitting. Some examples are provided to illustrate the main results.