The D1-Triangulation of Rn for Simplicial Algorithms for Computing Solutions of Nonlinear Equations

We present a new triangulation of ℝⁿ, which is called the D₁-triangulation, for computing zero points or fixed points of nonlinear mappings. The D₁-triangulation subdivides the unit cube and is based on very elementary pivot rules. We compare the D₁-triangulation to several well-known triangulations of ℝⁿ 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.