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

被引：0
|
作者：
Gao, Qinjiao [1 ,2 ]
Sun, Xingping [3 ]
Zhang, Shenggang [4 ]
机构：
[1] Zhejiang Gongshang Univ, Sch Stat & Math, Hangzhou 310018, Peoples R China
[2] Zhejiang Gongshang Univ, Collaborat Innovat Ctr Stat Data Engn Technol & A, Hangzhou 310018, Peoples R China
[3] Missouri State Univ, Dept Math, Springfield, MO 65897 USA
[4] Zhejiang Univ Sci & Technol, Sch Sci, Hangzhou 310023, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 404卷
基金：
中国国家自然科学基金;
关键词：
Concentration inequality; Ditzian-Totik modulus of smoothness; Order statistics; Stochastic Bernstein polynomial; APPROXIMATION; CONVERGENCE;
D O I：
10.1016/j.cam.2021.113888
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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