【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-x²）^-1/2)[ω(f′,n^-1（1-x²）^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。更多还原

【Abstract】 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’更多还原