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.

中文翻译：

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多元切比雪夫多项式的稀疏插值

稀疏插值}是指从有限数量的评估中将函数精确恢复为基函数的短线性组合。对于多元函数，单项式基的情况得到了很好的研究，就像现在指数函数的基一样。除了作为单变量 Chebyshev 多项式的张量积获得的多元 Chebyshev 多项式之外，根系统理论允许定义各种广义多元 Chebyshev 多项式，这些多项式与傅里叶分析和李代数表示等主题有关。我们提出了一种确定性算法来恢复一个函数，该函数是从 r 的知识和该函数的明确有界数量的评估中最多 r 个这样的多项式的线性组合。