Hermite-Fejér插值在一重积分Wiener空间下的平均误差

The Average Errors for Hermite-Fejér Interpolation on the 1-fold Integrated Wiener Space

本文在L_p-范数逼近意义下确定了一种Hermite-FIeér插值多项式列在一重积分Wiener空间下平均误差的弱渐近阶.结果显示在信息基复杂性的意义下,若可允许信息泛函为Hermite数据,则这种插值多项式列的平均误差在阶的意义下不是次最优的.

For the approximation in Lp-norm, we determined the weakly asymptotic order for the p-average errors of a kind of Hermite-Fejer interpolation sequence on the i-fold integrated Wiener space. By the result it is known that in the sense of Information-Based Complexity, if permissible information funetionals are Hermite data, then the p-average errors of this interpolation sequence are not suboptimal.