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On generalized bisection of $n$-simplices

Author: Reiner Horst
Journal: Math. Comp. 66 (1997), 691-698
MSC (1991): Primary 51M20, 90Bxx; Secondary 52B10, 65M50, 65N50, 90Cxx
MathSciNet review: 1388889
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Abstract: 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.

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Additional Information

Reiner Horst
Affiliation: Department of Mathematics, University of Trier, Trier 54286, Germany

Received by editor(s): May 10, 1995
Received by editor(s) in revised form: March 13, 1996
Article copyright: © Copyright 1997 American Mathematical Society