Stability of a distributed algorithm for solving linear algebraic equations

Ji Liu; A. Stephen Morse; Angelia Nedic; Tamer Basar

doi:10.1109/CDC.2014.7039966

Stability of a distributed algorithm for solving linear algebraic equations

Ji Liu, A. Stephen Morse, Angelia Nedic, Tamer Basar

Research output: Contribution to journal › Conference article › peer-review

Abstract

In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.

Original language	English (US)
Article number	7039966
Pages (from-to)	3707-3712
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2015-February
Issue number	February
DOIs	https://doi.org/10.1109/CDC.2014.7039966
State	Published - Jan 1 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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abstract = "In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.",

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AU - Morse, A. Stephen

AU - Nedic, Angelia

AU - Basar, Tamer

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AB - In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.

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