An analytic approach to estimating the solutions of Bézout's polynomial identity
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913198057193472 |
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| author | Fricain, Emmanuel Hartmann, Andreas Ross, William T. Timotin, Dan |
| author_facet | Fricain, Emmanuel Hartmann, Andreas Ross, William T. Timotin, Dan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12734 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An analytic approach to estimating the solutions of Bézout's polynomial identity Fricain, Emmanuel Hartmann, Andreas Ross, William T. Timotin, Dan Complex Variables Functional Analysis 30C10 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. |
| title | An analytic approach to estimating the solutions of Bézout's polynomial identity |
| topic | Complex Variables Functional Analysis 30C10 |
| url | https://arxiv.org/abs/2310.12734 |