关于Bernstein型插值过程的导数逼近

Derivative-Approximation by S. N. Bernstein-Interpolation Process

为插值节点的S.N.Bernstein型插值过程F_k(f,x)逼近函数f(x)时的收敛阶。一个十分有趣的问题是,F_n(f,x)的导数能否同时逼近函数f(x)的导数,且有较好的误差估计。

The aim of this paper is to detemine the convergence order of derivative approxi- mation by S. N. Bernstein interpolatory polynomial F_n(f,x) with zeros of Jacobi polynomial. The result is theorem.