论文标题
稀疏的插值在多元chebyshev多项式方面
Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials
论文作者
论文摘要
稀疏的插值}是指函数的精确恢复作为从有限数量的评估中的基础函数的短线性组合。对于多元函数，对单个基础的情况进行了充分的研究，现在是指数函数的基础。除了获得单变量Chebyshev多项式张量的多元多项式外，根系统的理论还可以定义各种通用多元化的Chebyshev多项式，这些多项式多项式与主题相关，例如傅立叶分析和lie Algebras的傅立叶分析和代表。我们提出了一种确定性算法，以恢复一个函数，该函数是从R的知识和明确界限的该功能评估数量的多项式组合的线性组合。
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.
