Metrics and norms used for obtaining sparse solutions to underdetermined Systems of Linear Equations

TL;DR

This paper explores metrics and norms for finding the sparsest solutions to underdetermined linear systems, extending metrics in n-dimensional spaces to improve solution sparsity.

Contribution

It introduces a new measure based on extending metrics via Cartesian products, aimed at obtaining optimal sparse solutions in underdetermined systems.

Findings

Proposes a novel metric for sparse solutions

Extends metrics in n-dimensional spaces for better sparsity

Applicable to algorithms for solving underdetermined systems

Abstract

This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product of metric spaces. *The following work done, was within the completion of my master thesis titled "Algorithms for the computation of sparse solutions of undefined systems of equations" at the department of Mathematics, University of Athens which was assigned to me in association with the department of Informatics and Telecommunications, National and Kapodistrian University of Athens.