Algebraic Connectivity Estimation Based on Decentralized Inverse Power Iteration

2016 ◽  
Vol 19 (2) ◽  
pp. 805-812
Author(s):  
Yue Wei ◽  
Hao Fang ◽  
Jie Chen ◽  
Bin Xin
Keyword(s):  
Inverse Power ◽  
Algebraic Connectivity ◽  
Power Iteration

Cooperative multi-agent search using Bayesian approach with connectivity maintenance

2019 ◽  
Vol 40 (1) ◽  
pp. 76-84
Author(s):  
Hu Xiao ◽  
Rongxin Cui ◽  
Demin Xu
Keyword(s):  
Bayesian Approach ◽  
Potential Field ◽  
Iteration Algorithm ◽  
Search Problem ◽  
Algebraic Connectivity ◽  
Content Type ◽  
Power Iteration ◽  
Gradient Based ◽  
Multi Agent ◽  
Connectivity Maintenance

Purpose This paper aims to present a distributed Bayesian approach with connectivity maintenance to manage a multi-agent network search for a target on a two-dimensional plane. Design/methodology/approach The Bayesian framework is used to compute the local probability density functions (PDFs) of the target and obtain the global PDF with the consensus algorithm. An inverse power iteration algorithm is introduced to estimate the algebraic connectivity λ2 of the network. Based on the estimated λ2, the authors design a potential field for the connectivity maintenance. Then, based on the detection probability function, the authors design a potential field for the search target. The authors combine the two potential fields and design a distributed gradient-based control for the agents. Findings The inverse power iteration algorithm can distributed estimate the algebraic connectivity by the agents. The agents can efficient search the target with connectivity maintenance with the designed distributed gradient-based search algorithm. Originality/value Previous study has paid little attention to the multi-agent search problem with connectivity maintenance. Our algorithm guarantees that the strongly connected graph of the multi-agent communication topology is always established while performing the distributed target search problem.

On controllability of the real shifted inverse power iteration

2001 ◽  
Vol 43 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Uwe Helmke ◽  
Fabian Wirth
Keyword(s):  
Inverse Power ◽  
Power Iteration ◽  
The Real

scholarly journals ADAPTIVE SOLUTION OF THE NEUTRON DIFFUSION EQUATION WITH HETEROGENEOUS COEFFICIENTS USING THE MIXED FINITE ELEMENT METHOD ON STRUCTURED MESHES

2021 ◽  
Vol 247 ◽  
pp. 02002
Author(s):  
Minh-Hieu Do ◽  
Patrick Ciarlet ◽  
François Madiot
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Diffusion Equation ◽  
Neutron Transport ◽  
Mesh Refinement ◽  
Generalized Eigenvalue Problem ◽  
Inverse Power ◽  
Computational Time ◽  
Power Iteration ◽  
Generalized Eigenvalue

The neutron transport equation can be used to model the physics of the nuclear reactor core. Its solution depends on several variables and requires a lot of high precision computations. One can simplify this model to obtain the SPN equation for a generalized eigenvalue problem. In order to solve this eigenvalue problem, we usually use the inverse power iteration by solving a source problem at each iteration. Classically, this problem can be recast in a mixed variational form, and then discretized by using the Raviart-Thomas-Nédélec Finite Element. In this article, we focus on the steady-state diffusion equation with heterogeneous coefficients discretized on Cartesian meshes. In this situation, it is expected that the solution has low regularity. Therefore, it is necessary to refine at the singular regions to get better accuracy. The Adaptive Mesh Refinement (AMR) is one of the most effective ways to do that and to improve the computational time. The main ingredient for the refinement techniques is the use of a posteriori error estimates, which gives a rigorous upper bound of the error between the exact and numerical solution. This indicator allows to refine the mesh in the regions where the error is large. In this work, some mesh refinement strategies are proposed on the Cartesian mesh for the source problem. Moreover, we numerically investigate an algorithm which combines the AMR process with the inverse power iteration to handle the generalized eigenvalue problem.

Inverse Power Law Behavior in a Memory Scanning Experiment

2006 ◽  
Author(s):  
Gerardo Ramirez ◽  
Sonia Perez ◽  
John G. Holden
Keyword(s):  
Power Law ◽  
Inverse Power ◽  
Memory Scanning ◽  
Inverse Power Law
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