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- W2002604535 abstract "This paper is concerned with the asymptotic behavior of $varphi (n)$, the minimum number of simplices required to triangulate the n-cube. Such triangulations are of special interest in connection with algorithms for approximating fixed points of continuous mappings. The standard triangulations of $I^n $ use $n!$ simplices. Let $H(n,m) = { x in R^n :sum {x_i = m} } $. Then $H(n,m)$ divides $I^n $ into two polytopes which are then triangulated in a certain fashion. If $K(n,m)$ is the cardinality of this triangulation, then lim $K ( n, n/2 ) /n! = 0$. Hence $varphi (n)$ is $o(n!)$. Another measure of the efficiency of a triangulation is the diameter of the dual graph and it is shown that this is $O(n^2 )$ for the above triangulation. Finally, a pivoting algorithm for the middle-cut triangulations of the n-cube is also presented." @default.
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- W2002604535 date "1984-09-01" @default.
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- W2002604535 title "The Middle-Cut Triangulations of the <i>n</i>-Cube" @default.
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- W2002604535 doi "https://doi.org/10.1137/0605039" @default.
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