Chebyshev Varieties
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929218490728448 |
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| author | Bel-Afia, Zaïneb Meroni, Chiara Telen, Simon |
| author_facet | Bel-Afia, Zaïneb Meroni, Chiara Telen, Simon |
| contents | Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defining equations of these varieties. We explain how they play the role of toric varieties in sparse polynomial root finding, when monomials are replaced by Chebyshev polynomials. We present numerical root finding algorithms that exploit our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chebyshev Varieties Bel-Afia, Zaïneb Meroni, Chiara Telen, Simon Algebraic Geometry Numerical Analysis Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defining equations of these varieties. We explain how they play the role of toric varieties in sparse polynomial root finding, when monomials are replaced by Chebyshev polynomials. We present numerical root finding algorithms that exploit our results. |
| title | Chebyshev Varieties |
| topic | Algebraic Geometry Numerical Analysis |
| url | https://arxiv.org/abs/2401.12140 |