The Schur complement of PH−matrices

Abstract

© 2019 Elsevier Inc. In this paper, we consider the class of PH−matrices, a subclass of H−matrices and, using scaling characterization, we show that this class is closed under taking the Schur complement. We show that, under certain conditions, the Perron complement of a PH−matrix is a PH−matrix. We also present a way of constructing a scaling matrix for the given PH−matrix and we give eigenvalue localization for the Schur complement of a PH−matrix using only the entries of the original matrix. We illustrate this by numerical examples.