2017/08/28 by Vladimir Temlyakov, Temlyakov, V. N.
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1708.08544
openalex publication_date 2017/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is devoted to discretization of integral norms of functions from a given collection of finite dimensional subspaces. For natural collections of subspaces of the multivariate trigonometric polynomials we construct sets of points, which are optimally (in the sense of order) good for each subspace of a collection from the point of view of the integral norm discretization. We call such sets universal. Our construction of the universal sets is based on deep results on existence of special nets, known as (t,r,d)-nets.