Some preconditioners for systems of linear inequalities

TL;DR

This paper investigates how combining simple preprocessing steps can improve the conditioning of homogeneous linear inequality systems by comparing different notions of conditioning.

Contribution

It introduces a novel approach that uses a combination of preprocessing steps to enhance the conditioning of linear inequalities.

Findings

Preprocessing improves system conditioning

Comparison among three conditioning notions

Enhanced numerical stability in solutions

Abstract

We show that a combination of two simple preprocessing steps would generally improve the conditioning of a homogeneous system of linear inequalities. Our approach is based on a comparison among three different but related notions of conditioning for linear inequalities.