Characterisations Of Certain Sign Regular Matrices

The class of sign regular matrices, as one of the important special matrices, is widely used in many fields. In this paper we consider the decomposition of rectangular sign regular matrices by Nevile elimination. The paper is organized as follows:In Chapter One, we present premilinaries and recent works on some decompositions of sign regular matrices by Neville eliminations;In Chapter Two, we present some basic notations and definitions about sign regular matrix, and discribe Neville elimination method.In Chapter Three, we provide LU factorizations of rectangular sign regular matrices with signature(1, 1, · · ·,-1) by Quasi-Neville elimination, and several examples are presented.In Chapter Four, we provide bidiagonal factorizations of rectangular sign regular matrices with signature(1, 1, · · ·,-1) by Neville elimination.