关于Bernstein-Grnwald插值过程的导数逼近  

On derivative approximation of interpolation process by Bernstein-Grünwald polynomial

作　　者：徐淳宁[1] 李宾[1] 

机构地区：[1]长春邮电学院基础部

出　　处：《长春邮电学院学报》1992年第2期42-46,共5页Journal of Changchun Post and Telecommunication Institute

摘　　要：研究了以第一类Chebyshev多项式T_n(x)的零点为插值节点的Bcrnstcin-Grunwald插值过程“1/2”平均算子G_n(f,x)的导数逼近。得到了|G_n′(f,x)-f′(x)|的误差估计: O((1-x^2)^(-1/2))[ω(f′,n^(-1)(1-x^2)^(1/2))+ω(f′,1/n)+1/n] 这里ω(f′,δ)是f′的连续模,“O”与n,x,f,f′无关。The derivative approximation of the interpolation process by '1/2' average Bernste in-Grilnwald polynomial operator, G,(f, x), which use zero of Chebyshev polynomial of the first kind as node is considered. The obtained error estimate of |Gn'(f,x)-f'(x)|isO((1-x2)-1/2)(w(f',n-11-x2+n-2)+w(f',n-1)+n-1),Where w(f',b) is modulus of continuty of f','0' independent of n, x, f,f'

关 键 词：多项式插值 导数 BG插值过程 

分 类 号：O174.42[理学—数学]