Random Sampling Scattered Data with Multivariate Bernstein Polynomials

作     者：Feilong CAO Sheng XIA 

作者机构：Department of Mathematics China Jiliang University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2014年第35卷第4期

页      面：607-618页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.61272023,61101240) the Innovation Foundation of Post-Graduates of Zhejiang Province(No.YK2011070) 

主　　题：Approximation Bernstein polynomials Random sampling Scattereddata 

摘      要：In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous fimction and Lp convergence for these operators are studied, respectively.