An analytic approach to estimating the solutions of B\'ezout's polynomial identity

Autor:	Fricain, Emmanuel, Hartmann, Andreas, Ross, William T., Timotin, Dan
Rok vydání:	2023
Předmět:	Mathematics - Complex Variables Mathematics - Functional Analysis 30C10
Druh dokumentu:	Working Paper
Popis:	This paper contains sharp bounds on the coefficients of the polynomials $R$ and $S$ which solve the classical one variable B\'{e}zout 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. Comment: 27 pages, 5 figures, updated references, updated funding acknowledgments
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.12734 Zobrazit plný text záznamu View this record from Arxiv