On generalized bisection of $n$-simplices
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- Math. Comp. 66 (1997), 691-698 Request permission
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.References
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Additional Information
- Reiner Horst
- Affiliation: Department of Mathematics, University of Trier, Trier 54286, Germany
- Email: horst@uni-trier.de
- Received by editor(s): May 10, 1995
- Received by editor(s) in revised form: March 13, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 691-698
- MSC (1991): Primary 51M20, 90Bxx; Secondary 52B10, 65M50, 65N50, 90Cxx
- DOI: https://doi.org/10.1090/S0025-5718-97-00809-0
- MathSciNet review: 1388889