$C^m$ convergence of trigonometric interpolants

[摘要] For m $\geq$ 0, we obtain sharp estimates of the uniform accuracy of the m-th derivative of the n-point trigonometric interpolant of a function for two classes of periodic functions on R. As a corrollary, the n-point interpolant of a function in $C^k$ uniformly approximates the function to order o($n^{1/2-k}$), improving the recent estimate of O($n^{1-k}$). These results remain valid if we replace the trigonometric interpolant by its K-th partial sum, replacing n by K in the estimates.

[学科分类] 计算机科学（综合）