On generalized bisection of n-simplices
On generalized bisection of n-simplices
复制标题
关于 n-单纯形的广义二分
DOI：
10.1090/s0025-5718-97-00809-0
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
R. Horst
中科院分区：
文献类型：
--
作者：
R. Horst
引入了 n-单纯形平分的广义过程，其中平分点可以是最长边之一处的（几乎）任意点。结果表明，由连续广义二分生成的单纯形的嵌套序列收敛到单例，并给出了以直径减小为单位的收敛速度的精确界限。对于标记最坏情况的正则单纯形，由连续二分生成的每个最差和最佳单纯形的边长度被给出至深度n。对于 n = 2 和 3，提供最坏情况直径的序列，直到其减半。
A generalized procedure of bisection of n-simplices is introduced, where the bisection point can be an (almost) arbitrary point at one of the longest edges. It is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton, and an exact bound of the convergence speed in terms of diameter reduction is given. For regular simplices, which mark the worst case, the edge lengths of each worst and best simplex generated by successive bisection are given up to depth n. For n = 2 and 3, the sequence of worst case diameters is provided until it is halved.