Weighting by iteration: iterations of n variables means based on subdivisions of the standard $$\left( n-1\right) $$-simplex

Abstract

The problem of weighting a general n variables mean is solved by using a class of algorithms which involve iterated subdivisions (triangulations) of the $$\left( n-1\right) $$ -simplex $$\Delta _{n-1}$$ . The instance based on the barycentric subdivision is treated at length, while a more sketchy presentation is given to the algorithm based on the Freudenthal triangulation. Generalizing the weightings of 2 variables means based on Aczel iterations, the resulting weighting procedures turn out to be continuous and scale invariant, being geometric the rate of convergence of the algorithms on the class of scaled uniformly internal means.