插值多项式在一重积分Wiener空间下的同时逼近平均误差
摘要
For the weighted <italic>L<sub>p</sub></italic>-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 areweakly equivalent to the average errors of the corresponding best polynomial approximation sequence for <italic>L<sub>p</sub></italic>-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 <italic>L<sub>p</sub></italic>-norm approximation (2≤<italic>p</italic>≤4). In comparison with these results, we determine asymptotical order of the average errors of the corresponding Hermite-Fejér interpolation sequence.