插值多项式在一重积分Wiener空间下的同时逼近平均误差

The simultaneous approximation average errors for interpolation polynomials on the 1-fold integrated Wiener space

本文在加权Lp范数逼近意义下确定了基于第一类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Lp范数逼近意义下Lagrange插值多项式列的平均误差弱等价于相应的最佳逼近多项式列的平均误差.同时,当2p4时,Lagrange插值多项式列导数逼近的平均误差弱等价于相应的导数最佳逼近多项式列的平均误差.作为对比,本文也确定了相应的Hermite-Fejér插值多项式列在一重积分Wiener空间下逼近的平均误差的渐近阶.

For the weighted Lp-norm approximation,we determine the asymptotical order for the simultaneous approximation average errors of Lagrange interpolation sequence based on the Chebyshev nodes on the 1-fold integrated Wiener space.By our results we know that the average errors of Lagrange interpolation sequence are weakly equivalent to the average errors of the corresponding best polynomial approximation sequence for Lp-norm approximation.At the same time,the average errors of the derivative approximation by Lagrange interpolation are weakly equivalent to the average errors of the corresponding best polynomial approximation sequence for Lp-norm approximation （2≤p≤4）.In comparison with these results,we determine asymptotical order of the average errors of the corresponding Hermite-Fejér interpolation sequence.