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arXiv · 2310.12734

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

Emmanuel Fricain·Andreas Hartmann·William T. Ross·Dan Timotin
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Abstract

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.

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Emmanuel Fricain, Andreas Hartmann, William T. Ross, Dan Timotin. 2023-10-19. An analytic approach to estimating the solutions of B\'ezout's polynomial identity. https://arxiv.org/abs/2310.12734

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