Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Foundations of Computational Mathematics Year : 2022

Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials

Michael F. Singer
  • Function : Author
  • PersonId : 1063598


Sparse interpolation refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now the basis of exponential functions. Beyond the multivariate Chebyshev polynomial obtained as tensor products of univariate Chebyshev polynomials, the theory of root systems allows to define a variety of generalized multivariate Chebyshev polynomials that have connections to topics such as Fourier analysis and representations of Lie algebras. We present a deterministic algorithm to recover a function that is the linear combination of at most r such polynomials from the knowledge of r and an explicitly bounded number of evaluations of this function.
Fichier principal
Vignette du fichier
HubertSinger2020_01.pdf (1.36 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02454589 , version 1 (24-01-2020)



Evelyne Hubert, Michael F. Singer. Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials. Foundations of Computational Mathematics, 2022, 22 (6), pp.1801-1862. ⟨10.1007/s10208-021-09535-7⟩. ⟨hal-02454589⟩
176 View
220 Download



Gmail Facebook X LinkedIn More