Search results for "Generalized mean"
showing 3 items of 3 documents
Distributed Consensus in Networks of Dynamic Agents
2006
Stationary and distributed consensus protocols for a network of n dynamic agents under local information is considered. Consensus must be reached on a group decision value returned by a function of the agents' initial state values. As a main contribution we show that the agents can reach consensus if the value of such a function computed over the agents' state trajectories is time invariant. We use this basic result to introduce a protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents' initial states. We demonstrate that the asymptotical consensus is reached via a Lyapunov approach. Finally we perfor…
Exploring students’ proof comprehension of the Cauchy Generalized Mean Value Theorem
2019
AbstractUndergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students’ proof comprehension, and Mejia-Ramos et al.’s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The test mainly focused on (a.) investigating students’ understanding of relations between the statements within the CGMVT proof and (b.) the relations between the CGMVT and other theorems. Thirty-five first-year university students voluntarily participated in this study. In addition, 10 of these students were subsequently interviewed to seek thei…
On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability
2021
Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…