A New Triangulation for Simplicial Algorithms

Triangulations are used in simplicial algorithms to nd the xed points of continuous functions or upper semi-continuous mappings; applications arise from economics and optimization. The performance of simplicial algorithms is very sensitive to the triangulation used. Using a facetal description, we modify Dang's D 1 triangulation to obtain a more eecient triangulation of the unit hypercube in R n and then by means of translations and reeections we derive a new triangulation, D 0 1 , of R n. We show that D 0 1 uses fewer simplices (asymptotically 30% fewer) than D 1 while achieving comparable scores for other performance measures such as the diameter and the surface density. We also compare the results of Haiman's recursive method for getting asymptotically better triangulations from D 1 , D 0 1 and other triangulations. Education of the Republic of Turkey through the scholarship program 1416.