Optimal stochastic Bernstein polynomials in Ditzian-Totik type modulus of smoothness
Gao, Qinjiao 1Sun, Xingping 2Zhang, Shenggang3
扫码查看
点击上方二维码区域，可以放大扫码查看
作者信息
1. Zhejiang Gongshang Univ
2. Missouri State Univ
3. Zhejiang Univ Sci & Technol
折叠
Abstract
We introduce a family of symmetric stochastic Bernstein polynomials based on order statistics, and establish the order of convergence in probability in terms of the second order Ditzian-Totik type modulus of smoothness on the interval [0, 1], which epitomizes an optimal pointwise error estimate for the classical Bernstein polynomial approximation. Monte Carlo simulation results (presented at the end of the article) show that this new approximation scheme is efficient and robust. (C) 2021 Elsevier B.V. All rights reserved.
Key words
Concentration inequality/Ditzian-Totik modulus of smoothness/Order statistics/Stochastic Bernstein polynomial/APPROXIMATION/CONVERGENCE
NSTL
Elsevier