Dang, Chuangyin The \(D_ 1\)-triangulation of \({\mathbb{R}}^ n\) for simplicial algorithms for computing solutions of nonlinear equations. (English) Zbl 0734.90121 Math. Oper. Res. 16, No. 1, 148-161 (1991). 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. Cited in 1 ReviewCited in 8 Documents 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 Keywords:triangulation; fixed points of nonlinear mappings; measures of efficiency; diameter; average directional density; surface density PDFBibTeX XMLCite \textit{C. Dang}, Math. Oper. Res. 16, No. 1, 148--161 (1991; Zbl 0734.90121) Full Text: DOI