ON A BIVARIATE B-SPLINE BASIS
ON A BIVARIATE B-SPLINE BASIS
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DOI：
10.1360/ya1984-27-11-1129
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发表时间：
1984-11
期刊：
影响因子：
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通讯作者：
Cui Jin-Tai;Wang Ren-hong
中科院分区：
文献类型：
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作者：
Cui Jin-Tai;Wang Ren-hong
虽然在矩形网格划分fork≥3的三角剖分细化Δmn上不存在非平凡的k次二元C k-1样条函数，但给出了网格划分均匀时具有最小对称支撑的二元C 1 二次B样条函数的基础。此外，还给出了 B 样条恒等式，其中包括单变量样条的 Marsden 恒等式的推广。这些恒等式使我们能够给出网格划分为 △ mn 的 C 1 二次样条函数的整个空间的近似误差估计，并给出渐近公式。
While there does not exist any nontrivial locally supported bivariate C k-1 splinefunction of degree k on a triangulation refinement △ mn of a rectangular grid partition fork≥3, a basis of bivariate C 1 quadratic B-splines with smallest symmetric supports isgiven when the grid partition is uniform. In addition, B-spline identities which include ageneralization of Marsden's identity for univariate splines are given. These identities en-able us to give error estimates for approximation from the entire space of C 1 quadraticspline functions with grid partition △ mn and to give asymptotic formulas.