An analytic approach to estimating the solutions of Bézout's polynomial identity
| hal.structure.identifier | Laboratoire Paul Painlevé - UMR 8524 [LPP] | |
| dc.contributor.author | FRICAIN, Emmanuel | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HARTMANN, Andreas | |
| hal.structure.identifier | University of Richmond | |
| dc.contributor.author | ROSS, William | |
| hal.structure.identifier | Simon Stoilow Institute of Mathematics of the Romanian Academy | |
| dc.contributor.author | TIMOTIN, Dan | |
| dc.date.accessioned | 2024-04-04T02:32:58Z | |
| dc.date.available | 2024-04-04T02:32:58Z | |
| dc.date.created | 2023 | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190434 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Noyaux reproduisants en Analyse et au-delà - ANR-18-CE40-0035 | |
| dc.description.sponsorship | Centre Européen pour les Mathématiques, la Physique et leurs Interactions - ANR-11-LABX-0007 | |
| dc.language.iso | en | |
| dc.subject.en | Bézout identity | |
| dc.subject.en | Cauchy integral formula | |
| dc.subject.en | Sylvester matrix | |
| dc.subject.en | Corona theorem | |
| dc.title.en | An analytic approach to estimating the solutions of Bézout's polynomial identity | |
| dc.type | Document de travail - Pré-publication | |
| dc.identifier.doi | 10.48550/arXiv.2310.12734 | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2310.12734 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04251996 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04251996v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023&rft.au=FRICAIN,%20Emmanuel&HARTMANN,%20Andreas&ROSS,%20William&TIMOTIN,%20Dan&rft.genre=preprint |
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