Lagrange插值和Hermite-Fejér插值在Wiener空间下的平均误差

许贵桥;

数学学报 ›› 2007, Vol. 50 ›› Issue (6) : 1281-129.

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PDF(464 KB)
数学学报 ›› 2007, Vol. 50 ›› Issue (6) : 1281-129. DOI: 10.12386/A2007sxxb0151
论文

Lagrange插值和Hermite-Fejér插值在Wiener空间下的平均误差

    许贵桥;
作者信息 +

The Average Error for Lagrange Interpolation and Hermite-Fejér Interpolation on the Wiener Space

    Gui Qiao XU
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摘要

在L_q-范数逼近的意义下,确定了基于Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差的弱渐近阶.从我们的结果可以看出,当2≤q<∞,1≤p<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列的p-平均误差弱等价于相应的最佳逼近多项式列的p-平均误差.在信息基计算复杂性的意义下,如果可允许信息泛函为计算函数在固定点的值,那么当1≤p,q<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差弱等价于相应的最小非自适应p-平均信息半径.

Abstract

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.

关键词

Lagrange插值 / Chebyshev多项式 / Hermite-Fejér插值

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许贵桥;. Lagrange插值和Hermite-Fejér插值在Wiener空间下的平均误差. 数学学报, 2007, 50(6): 1281-129 https://doi.org/10.12386/A2007sxxb0151
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
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