【摘要】 本文以文献[1—3]为基础,进一步讨论了用Hermite-Fejèr插值多项式逼近连续函数f(x)∈C[-1,1]的收敛阶问题。当,f′(x)∈C[-1,1]时,文中给出收敛阶的误差估计并且证明了这种估计对于某一连续函数类不可再改进。更多还原

【Abstract】 Based on the articles [1—3], in this paper we discuss the problem about precision of approximation to f(x)∈C [-1,1] by the Hermite-Fejér interpolatory polynomial H_n(f;x). This paper gives an estimate of the convergence order of H_n(f;x) when f’(x)∈C[-1,1] and shows that this estimate can not be improved with respect to certain class of continuous function.更多还原