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Distributed Linear Equations Over Random Networks
- Source :
- IEEE Transactions on Automatic Control. 68:2607-2614
- Publication Year :
- 2023
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2023.
-
Abstract
- Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research attention. Communications over a network have a stochastic nature, with both temporal and spatial dependence due to link failures, packet dropouts or node recreation, etc. In this paper, we study the convergence and convergence rate of distributed linear equation protocols over a $\ast$-mixing random network, where the temporal and spatial dependencies between the node-to-node communications are allowed. When the network linear equation admits exact solutions, we prove the mean-squared exponential convergence rate of the distributed projection consensus algorithm, while the lower and upper bound estimations of the convergence rate are also given for independent and identically distributed (i.i.d.) random graphs. Motivated by the randomized Kaczmarz algorithm, we also propose a distributed randomized projection consensus algorithm, where each node randomly selects one row of local linear equations for projection per iteration, and establish an exponential convergence rate. When the network linear equation admits no exact solution, we prove that a distributed gradient-descent-like algorithm with diminishing step-sizes can drive all nodes' states to a least-squares solution at a sublinear rate. These results collectively illustrate that distributed computations may overcome communication correlations if the prototype algorithms enjoy certain contractive properties or are designed with suitable parameters.<br />17 pages
- Subjects :
- FOS: Computer and information sciences
Computer Science - Distributed, Parallel, and Cluster Computing
Optimization and Control (math.OC)
Control and Systems Engineering
FOS: Mathematics
Distributed, Parallel, and Cluster Computing (cs.DC)
Electrical and Electronic Engineering
Mathematics - Optimization and Control
Computer Science Applications
Subjects
Details
- ISSN :
- 23343303 and 00189286
- Volume :
- 68
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Automatic Control
- Accession number :
- edsair.doi.dedup.....99f1505e751a84a7732305f8a1bd1f98