For the Lq-norm approximation,we determine the weakly asymptoticl order for the p-average errors of the Lagrange interpolation sequence and the Hermite-Fejér interpolation sequence based on the Chebyshev nodes on the Wiener space.By these results we know that for 2(?)q<∞,1(?)p<∞,the p-average errors of Lagrange interpolation sequence and Hermite-Fejér interpolation sequence based on the Cheby- shev nodes are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence.In the sense of Information-Based Complexity,if permissible information functionals are function evaluations at fixed points,then the p-average errors of Lagrange interpolation sequence and Hermite-Fejér interpolation sequence based on the Chebyshev nodes are weakly equivalent to the corresponding sequence of minimal p-average radii of nonadaptive information.
Gui Qiao XU.
The Average Error for Lagrange Interpolation and Hermite-Fejér Interpolation on the Wiener Space. Acta Mathematica Sinica, Chinese Series, 2007, 50(6): 1281-129 https://doi.org/10.12386/A2007sxxb0151