The closure property of the Schur complement for Nekrasove matrices and its applications in solving large linear systems with Schur-based method

Abstract

In this paper, several conditions are presented to keep the Schur complement via a non-leading principle submatrix of some special matrices including Nekrasov matrices being a Nekrasov matrix, which is useful in the Schur-based method for solving large linear equations. And we give some infinity norm bounds for the inverse of Nekrasov matrices and its Schur complement to help measure whether the classical iterative methods are convergent or not. At last, in the applications of solving large linear equations by Schur-based method, some numerical experiments are presented to show the efficiency and superiority of our results.