Improvement of a Distributed Algorithm for Solving Linear Equations

This paper performs further improvement to a distributed algorithm for solving linear algebraic equations via multi-agent networks recently developed by Mou et al., in which all agents' states converge exponentially fast to the same solution to a group of linear equations by assuming each agent...

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Bibliographic Details
Published in:IEEE transactions on industrial electronics (1982) Vol. 64; no. 4; pp. 3113 - 3117
Main Authors: Wang, Xuan, Mou, Shaoshuai, Sun, Dengfeng
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Convex functions
Decentralized control
Distributed algorithms
Euclidean distance
Euclidean geometry
Kernel
Linear algebra
Linear equations
Mathematical analysis
multi-agent network
Multiagent systems
Process control
Sun
ISSN:0278-0046, 1557-9948
Online Access:Get full text
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Summary:This paper performs further improvement to a distributed algorithm for solving linear algebraic equations via multi-agent networks recently developed by Mou et al., in which all agents' states converge exponentially fast to the same solution to a group of linear equations by assuming each agent knows only part of the linear equations and its nearby neighbors' states. We first prove that the algorithm proposed by Mou et al. with special initialization is able to achieve the solution that is closest to a given point in the Euclidean distance. Second, we eliminate the required initialization step used by Mou et al. by a modification to the update equation. Both analytical and numerical results are provided for validation.
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ISSN:0278-0046
1557-9948
DOI:10.1109/TIE.2016.2636119