An analytic approach to estimating the solutions of Bézout's polynomial identity

2023/10/19 by Emmanuel Fricain, Andreas Hartmann, Fricain, Emmanuel +5
Computer Science · Mathematics · #30C10 #Advanced Optimization Algorithms Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2310.12734

openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper contains sharp bounds on the coefficients of the polynomials R and S which solve the classical one variable Bézout identity A R + B S = 1, where A and B are polynomials with no common zeros. The bounds are expressed in terms of the separation of the zeros of A and B. Our proof involves contour integral representations of these coefficients. We also obtain an estimate on the norm of the inverse of the Sylvester matrix.

Related

• Bézout Identities Associated to a Finite Sequence
• Several Applications of Bezout Matrices
• Three quantities arising from Bézout's identity and resultants of integer polynomials
• The Structure of the Inverse to the Sylvester Resultant Matrix
• A proof of the main theorem on Bezoutians