关于一类插值多项式的最高收敛阶(英文)

On the Best Convergence Order of a Kind of Interpolation Process

以第一类Tchebyshev多项式的零点作为插值节点 ,推广了伯恩斯坦提出的一个问题 ,构造了插值多项式算子Gn ,b(f ;x) ,它不仅对 f(x) ∈Ca[- 1,1] (0 a b - 1,其中 b为自然数 )一致收敛 ,而且收敛阶达到了最佳。对算子Gn ,b(f ;x) ,最高收敛阶不会超过 1/nb 。

A problem of Bernstein is generalized. An interpolation polynomial operator Gn,b(f;x) is constructed which based on the zeros of the first kind of Tchebshev polynomial as the interpolation nodes. It converges to f(x) ε C[-1,1]1, (0 [less-than or equal to] a [less-than or equal to] b - 1) uniformly and the convergence order is the best (where b is a nature).