Polynomial approximation on C²-domains

2019/10/25 by Feng Dai, Andriy Prymak, Dai, Feng +1
Computer Science · Mathematics · #41A10 #41A17 #41A27 #41A55 #41A63 (Primary) #65D32 (Secondary) #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1910.11719

openalex publication_date 2019/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact C²-domain Ω⊂ ℝ^d. This new modulus of smoothness is defined via finite differences along the directions of coordinate axes, and along a number of tangential directions from the boundary. With this modulus, we prove both the direct Jackson inequality and the corresponding inverse for best polynomial approximation in L_p(Ω). The Jackson inequality is established for the full range of 0

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