High-dimensional periodic sampling on Smolyak grids based on B-spline quasi-interpolation

2015/02/05 by Ðinh Dũng, Dũng, Dinh
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1502.01447

openalex publication_date 2015/02/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We constructed linear algorithms of sampling recovery and cubature formulas on Smolyak grids parametrized by m ∈ ℕ of periodic d-variate functions having Lipschitz-Hölder mixed smoothness α> 0 based on B-spline quasi-interpolation, and studied their optimality. We established lower estimates (for α≤ 2) and upper bounds of the error of the optimal sampling recovery and the optimal integration on Smolyak grids, explicit in d, m and the number ν of active variables of functions when d and m may be large.

Citations

• Sampling and cubature on sparse grids based on a B-spline\n quasi-interpolation

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