Chebyshev Varieties
Algebraic Geometry
2024-01-23 v1 Numerical Analysis
Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2401.12140,
title = {Chebyshev Varieties},
author = {Zaïneb Bel-Afia and Chiara Meroni and Simon Telen},
journal= {arXiv preprint arXiv:2401.12140},
year = {2024}
}
Comments
27 pages, 11 figures