. C O ] 1 1 A pr 2 00 2 ASYMPTOTICALLY EFFICIENT TRIANGULATIONS OF THE d - CUBE
نویسنده
چکیده
We describe a method to triangulate P × Q which is very useful to obtain triangulations of the d-cube I of good asymptotic efficiency. The main idea is to triangulate P × Q from a triangulation of Q and another of P ×∆, where ∆ is a simplex of dimension m− 1, which is supposed to be smaller than dim(Q) = n− 1. Last triangulation will induce a triangulation of P ×∆. Thus, considering P := I and Q := I we obtain a triangulation of I. Using a convenient triangulation of I ×∆ with 38 simplices we obtain that, asymptotically, the d-cube can be triangulated with 0.816d! simplices, instead of the 0.840d! achievable before.
منابع مشابه
Asymptotically efficient triangulations of the d-cube
Triangulating the regular d-cube I = [0, 1] in a “simple” way has many applications, like solving differential equations by finite element methods or calculating fixed points. See, for example, [7]. Determining the smallest number of simplices needed has brought special attention both from a theoretical point of view and from an applied one (see [6, Section 14.5.2] for a recent survey). Before ...
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