A networked parallel algorithm for solving linear algebraic equations

Solving a system of linear algebraic equations is a fundamental problem, especially when there is a large number of design variables. To this purpose, we consider a collaborative framework with multiple interconnected agents that are distributed among different nodes of a network, and each agent mai...

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Bibliographic Details
Published in:	2016 IEEE 55th Conference on Decision and Control (CDC) pp. 1727 - 1732
Main Authors:	Keyou You, Shiji Song, Tempo, Roberto
Format:	Conference Proceeding
Language:	English Japanese
Published:	IEEE 01.12.2016
Subjects:	Algorithm design and analysis Convergence Distributed algorithms Google Mathematical model Optimization Parallel algorithms
Online Access:	Get full text
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Summary:	Solving a system of linear algebraic equations is a fundamental problem, especially when there is a large number of design variables. To this purpose, we consider a collaborative framework with multiple interconnected agents that are distributed among different nodes of a network, and each agent maintains a state vector to compute the solution. Under local interactions, we propose an iterative algorithm for each agent to update the state vector via a convex combination of a consensus mechanism and a projector, which pushes the state vector toward a local constraint set. We show the linear convergence to the solution if the network is strongly connected for fixed graphs or uniformly jointly strongly connected for time-varying graphs. As an important application, we adopt this algorithm to distributedly solve the Google's PageRank problem. Moreover, we discuss the implications and relations to the relevant literature.
DOI:	10.1109/CDC.2016.7798514