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" Analysis of a Distributed Algorithm for Solving Linear Equations "
Duru, Osman Mecnun
Cihan, Onur
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Latin Dissertation
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English
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| Record Number
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1055478
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| Doc. No
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TL54595
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| Main Entry
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Duru, Osman Mecnun
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| Title & Author
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Analysis of a Distributed Algorithm for Solving Linear Equations\ Duru, Osman MecnunCihan, Onur
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| College
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Marmara Universitesi (Turkey)
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| Date
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2019
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| Degree
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Master's
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| student score
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2019
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| Note
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68 p.
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| Abstract
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Solving a linear equation system is one of the most known and important problems in science and engineering. Such systems have numerous applications such as forecasting, estimation and linear approaches to nonlinear equations. For the solution of these systems, several distributed algorithms have been proposed in the literature, which divide large linear equation systems into small pieces and enable them to be solved faster and more accurately than solving it by a centralized processor. The basic idea of these algorithms is to consider the system as a multi-agent network structure where the autonomous agents are physically separated from each other and communicate with their neighbors nearby. The network consists of multiple agents, each agent knows only a subset of the equation and therefore none can solve the overall equation individually. In order to overcome this issue, all agents must work cooperatively in a distributed way. Each agent i has a solution vector x_i (t) that takes values in R^n, and it is assumed that the only information that the agent receives from its neighbor j is its state vector. The aim of the thesis is to upgrade a well-known distributed algorithm in [1] for solving a linear algebraic equation and investigate its convergence rate. In this thesis, we consider a distributed algorithm and examine its convergence rate in networks with and without transmission delays. A new rapid method is proposed for both cases. Convergence rates of a well-known algorithm in the literature and the one proposed in this thesis are compared for un-delayed and delayed networks. Furthermore, the effect of weighting strategies on the convergence rate of the algorithm is investigated for several important network topologies as well and it is shown that for all topologies under consideration, the random walk method yields the fastest convergence for the example equation system.
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Electrical engineering
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Systems science
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Cihan, Onur
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Marmara Universitesi (Turkey)
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