Lagrange插值在—重积分Wiener空间下的同时逼近平均误差

在加权L_p范数逼近意义下,确定了基于扩充的第二类Chebyshev结点组的Lagrange插值多项式列,在一重积分Wiener空间下同时逼近平均误差的渐近阶.结果显示,在L_p范数逼近意义下,Lagrange插值多项式列逼近函数及其导数的平均误差都弱等价于相应的最佳逼近多项式列的平均误差.同时,在信息基复杂性的意义下,若可允许信息泛函为标准信息,则上述插值算子列逼近函数及其导数的平均误差均弱等价于相应的最小非自适应信息半径.

The Simultaneous Approximation Average Errors of Lagrange Interpolation on the 1-fold Integrated Wiener Space

In this paper,for weighted approximation in L_p-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Lagrange interpolation sequence which based on the extended Chebyshev nodes of the second kind on the 1-fold integrated Wiener space. These results show that the average errors of both function approximation and derivative approximation by above mentioned Lagrange interpolation sequence are weakly equivalent to the average errors of the corresponding best polynomial approximation sequence for approximation in L_p-norm.In the sense of Information-Based Complexity, if permissible information functionals consist of standard information,then the average errors of both function approximation and derivative approximation by above mentioned interpolation sequence are weakly equivalent to the corresponding sequences of minimal average radii of nonadaptive information.