三方向网格上二元基插值的收敛性及误差估计

Convergence and Error Estimation of Bivariate Cardinal Interpolation on a Three-Direction Mesh

本文讨论了平面的三方向正则网格上二元箱样条的基插值及其导数问数,改进和推扩了 dc Boor 及 H(?)llig 等人的结果,然后给出了当“次数趋于无穷”时基插值的收敛性及误差估计。

The purpose of this paper is to discuss the problem of bivariate cardinal interpolation by box splines and their derivatives on a three-direction regular mesh on R^2. We improve and generalize the results given by de Boor,H(?)lling and the others,and in particular give the convergence and the error estimation of this cardinal interpolation as the degree tends to inhnity.