A Non-Triviality Certificate for Scalars and its application to Linear Systems

TL;DR

This paper introduces a novel non-triviality certificate for scalars, utilizing asymptotic weighted averages, and applies it to develop an efficient algorithm for feasibility analysis of linear inequality systems.

Contribution

It presents a new approach to certify non-triviality of scalars and leverages it to create an O(M^4) algorithm for linear system feasibility and variable subset analysis.

Findings

Developed a non-triviality certificate based on asymptotic weighted averages.

Created an O(M^4) algorithm for feasibility of linear inequalities.

Enabled analysis of non-trivial solutions for variable subsets.

Abstract

We present an approach of taking a linear weighted Average of N given scalars, such that this Average is zero, if and only if, all N scalars are zero. The weights for the scalars in this Average vary asymptotically with respect to a large positive real. We use this approach with a previous result on Asymptotic Linear Programming, to develop an O(M^4) Algorithm that decides whether or not a system of M Linear Inequalities is feasible, and, whether or not any desired subset of the variables in this system, is permitted to have a non-trivial solution.