一些特殊三角剖分上分片线性样条的最佳逼近问题

Tchebyshev Approximation by $S_1^0(\Delta)$ over Some Special Triangulations

中文关键词:  最佳逼近  二元样条  $S_1^0(\Delta)$.

英文关键词:Tchebyshev approximation  bivariate splines  $S_1^0(\Delta)$.

中文摘要:

      关键点组的概念在最佳逼近理论中起着至关重要的作用.一般来说,在多元最佳逼近理论中,要判别一个点组是否为关键点组是不容易的.本文刻画了一些三角剖分上分片线性样条的最佳逼近的具体特征,此特征可有效地用于判读一个分片线性函数是否为该三角剖分上的最佳逼近.

英文摘要:

      The critical point set plays a central role in the theory of Tchebyshev approximation. Generally, in multivariate Tchebyshev approximation, it is not a trivial task to determine whether a set is critical or not. In this paper, we study the characterization of the critical point set of $S_1^0(\Delta)$ in geometry, where $\Delta$ is restricted to some special triangulations (bitriangular, single road and star triangulations). Such geometrical characterization is convenient to use in the determination of a critical point set.