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The \(D_ 1\)-triangulation of \({\mathbb{R}}^ n\) for simplicial algorithms for computing solutions of nonlinear equations. (English) Zbl 0734.90121

Summary: We present a new triangulation of \({\mathbb{R}}^ n\), which is called the \(D_ 1\)-triangulation, for computing zero points or fixed points of nonlinear mappings. The \(D_ 1\)-triangulation subdivides the unit cube and is based on very elementary pivot rules. We compare the \(D_ 1\)- triangulation to several well-known triangulations of \({\mathbb{R}}^ n\) which triangulate the unit cube. According to several measures of efficiency the new triangulation is superior, such as the number of simplices in the unit cube, the diameter of a triangulation, the average directional density, and the surface density.

MSC:

90C99 Mathematical programming
65H10 Numerical computation of solutions to systems of equations
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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