矩形域上散乱数据多元最优插值的误差估计及其超收敛性（Ⅰ）──带连续边界条件

SUPERCONVERGENCE AND ERROR BOUNDS FOR THE MULTIVARIATE OPTIMAL INTERPOLATION TO SCATTERED DATA THROUGHOUT A RECTANGLE (I)- WITH CONTINUOUS BOUNDARY CONDITIONS

本文我们讨论了矩形域上带连续边界条件的一类多元散乱数据最优插值。给出了某些情形插值的误差估计，误差估计表明在某些点上还具有超收敛性。

In this paper, the multivariate smoothing interpolation to scattered data proposed in [2] is considered. For these methods,error bounds are studied and some superconvergence points are also found under some particular circumstances.