Arithmetic functions and weighted averages

Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions

Characteristic Functions and Averages

Let Ω be a set and Ω1, . . . ,Ωm−1 subsets of Ω, being m an integer greater than one. For a given function f = (f1, . . . fm) : Ω → R, we prove the existence of a unique function α = (α1, . . . , αm) : Ω → R m such that

Weighted Averages and Double Exponential Algorithms

This paper reviews two simple numerical algorithms particularly useful in Computational ElectroMagnetics (CEM): the Weighted Averages (WA) algorithm and the Double Exponential (DE) quadrature. After a short historical introduction and an elementary description of the mathematical procedures underlying both techniques, they are applied to the evaluation of Sommerfeld integrals, where WA and DE c...

Convergence of Weighted Averages of Relaxed Projections

The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods. Examples illustrating these generalizations are given.

Asymmetric network connectivity using weighted harmonic averages

We propose a non-metric measure of the “closeness” felt between two nodes in an undirected, weighted graph using a simple weighted harmonic average of connectivity, that is a realvalued Generalized Erdös Number (GEN). While our measure is developed with a collaborative network in mind, the approach can be of use in a variety of artificial and real-world networks. We are able to distinguish betw...