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

Optimal stochastic Bernstein polynomials in Ditzian-Totik type modulus of smoothness
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DOI：
10.1016/j.cam.2021.113888
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发表时间：
2021-10
期刊：
J. Comput. Appl. Math.
影响因子：
--
通讯作者：
Qinjiao Gao;Xingping Sun;Shenggang Zhang
Qinjiao Gao;Xingping Sun;Shenggang Zhang
中科院分区：
其他
文献类型：
--
作者：
Qinjiao Gao;Xingping Sun;Shenggang Zhang

文献摘要

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引入了一类基于顺序统计量的对称随机Bernstein多项式，并利用区间[0，1]上的二阶Ditzian-Totik型光滑模建立了收敛的概率阶，推广了经典Bernstein多项式逼近的点态误差估计.蒙特卡罗模拟结果表明，这种新的近似方案是有效和稳健的。
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.