Non-uniform non-asymptotical sharp estimate for the rate of convergence for Bernstein's polynomial approximation, with bilateral constant evaluation

2015/08/27 by E. Ostrovsky, Eugene Ostrovsky, Ostrovsky, Eugene +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Iterative Methods for Nonlinear Equations #Statistical and numerical algorithms #math.FA

paper · pdf · doi:10.48550/arxiv.1508.06933

arXiv admin note: text overlap with arXiv:1406.3933

arxiv created 2015/08/27 · openalex publication_date 2015/08/27 · arxiv updated 2015/08/31 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

We derive the non-asymptotical non-uniform sharp error estimation for Bernstein's approximation of continuous function based on the modern probabilistic apparatus. We investigate also the convergence of derivative of these polynomials and we will consider briefly also the multivariate case.

Citations

• Subgaussian and strictly subgaussian random variable

Cited by

• Generalized Bernstein-type approximation of continuous functions

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