An analytic approach to estimating the solutions of Bézout's polynomial identity
Emmanuel Fricain, Hartmann, Andreas, William T. Ross, Dan Timotin · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
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.