Backward stability with almost strictly sign regular matrices

Abstract

A sign regular matrix is almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign. These matrices form a subclass of sign regular matrices (matrices whose minors of the same order have the same sign). In this paper, the backward stability for almost strictly sign regular matrices is studied when Neville elimination with two-determinant pivoting strategy is applied. In addition, several numerical experiments are also presented.