Infinity norm bounds for the inverse of Nekrasov matrices using scaling matrices

TL;DR

This paper develops new bounds for the inverse of Nekrasov matrices using scaling matrices, improving existing error bounds for related linear complementarity problems through theoretical analysis and numerical validation.

Contribution

It introduces a novel approach employing scaling matrices to derive tighter infinity norm bounds for Nekrasov matrices and their inverses, enhancing error estimates in linear complementarity problems.

Findings

Derived new infinity norm bounds for Nekrasov matrices' inverses.

Numerical examples demonstrate the bounds' effectiveness and improvements over previous methods.

Improved error bounds for linear complementarity problems involving Nekrasov matrices.

Abstract

For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly diagonally dominant matrix. Numerical examples and comparisons with other bounds are included. The scaling matrices are also used to derive new error bounds for the linear complementarity problems when the involved matrix is a Nekrasov matrix. These error bounds can improve considerably other previous bounds.