The accurate and efficient solutions of linear systems for generalized sign regular matrices with certain signature

Abstract

In this paper, we consider how to accurately solve the linear system whose coefficient matrix is a generalized sign regular (GSR) matrix with signature (1,…,1,−1). A new algorithm with O(n2) complexity is presented to solve the GSR linear system, provided that parameterization matrices of coefficient matrices are available. We illustrate that no subtraction-cancellation occurs in the computations of the algorithm, which guarantees that all the solution components are computed with a desirable accuracy. An error analysis and numerical experiments are presented to confirm the high accuracy.