R\'esolution des syst\`emes polynomiaux: un solveur bas\'e sur les matrices de Bezout

TL;DR

This paper introduces a linear algebra-based algorithm using Bezout matrices to compute numerical solutions of polynomial systems in complete intersection, enabling floating point computations with a full implementation provided.

Contribution

It presents a novel method leveraging Bezout matrices for solving polynomial systems efficiently in floating point arithmetic.

Findings

Algorithm successfully computes solutions in floating point.

Implementation demonstrates practical applicability.

Method simplifies solving polynomial systems using linear algebra.

Abstract

We propose a method to compute the numerical solutions of a polynomial system in complete intersection. This algorithm makes use of Bezout matrices and need only linear algebra computations. All the calculations can be done in floating point arithmetic. A complete implementation of the algorithm is provided.