An Algorithm for Finding Positive Solutions to Polynomial Equations

TL;DR

This paper introduces a numerical algorithm that leverages statistical techniques like expectation maximization and iterative proportional fitting to find approximate non-negative solutions to polynomial equations, especially in overconstrained systems.

Contribution

It presents a novel application of statistical algorithms to polynomial equations, enabling approximate solutions where exact solutions do not exist.

Findings

Effective in finding approximate solutions for overconstrained systems

Utilizes expectation maximization and iterative proportional fitting algorithms

Applicable to real non-negative solutions of polynomial equations

Abstract

We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find maximum likelihood parameters for certain classes of statistical models. Since our algorithm works by iteratively improving an approximate solution, we find approximate solutions in the cases when there are no exact solutions, such as overconstrained systems.