Optimal stochastic Bernstein polynomials in Ditzian-Totik type modulus of smoothness

DOI10.1016/j.cam.2021.113888zbMath1492.60206OpenAlexW3211057102MaRDI QIDQ2059641

Xingping Sun, Shenggang Zhang, Qinjiao Gao

Publication date: 14 December 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113888

zbMATH Keywords

order statisticsconcentration inequalityDitzian-Totik modulus of smoothnessstochastic Bernstein polynomial

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Summability in several variables (42B08)

Cites Work

• Über den Grad der Approximation mit Bernstein-Polynomen
• Der Wert einiger Konstanten in der Theorie der Approximation mit Bernstein-Polynomen
• Estimates of positive linear operators in terms of second-order moduli
• Piecewise linear approximation methods with stochastic sampling sites
• Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates
• Polynomial convergence order of stochastic Bernstein approximation
• Stochastic Bernstein polynomials: uniform convergence in probability with rates
• On the mathematical foundations of learning
• Learning Theory
• Approximation by Bernstein Polynomials
• Order Statistics
• Chebyshev type inequality for stochastic Bernstein polynomials
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• Upper estimates in direct inequalities for Bernstein-type operators
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