A Distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks
| Autor: | Nicola Elia, Seyyed Shaho Alaviani |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Random graph 0209 industrial biotechnology Iterative method Computer science Block matrix 020206 networking & telecommunications 02 engineering and technology Computer Science Applications Matrix (mathematics) Algebraic equation 020901 industrial engineering & automation Convergence of random variables Control and Systems Engineering Distributed algorithm Limit point Convex optimization 0202 electrical engineering electronic engineering information engineering Applied mathematics Almost surely Electrical and Electronic Engineering Convex function Mathematics |
| Zdroj: | CDC |
| ISSN: | 2334-3303 0018-9286 |
| Popis: | This article considers the problem of solving linear algebraic equations of the form $Ax=b$ among multiagents, which seek a solution by using local information in presence of random communication topologies. The equation is solved by $m$ agents where each agent only knows a subset of rows of the partitioned matrix $[A,b]$ . The problem is formulated such that this formulation does not need the distribution of random interconnection graphs. Therefore, this framework includes asynchronous updates and/or unreliable communication protocols. The random Krasnoselskii–Mann iterative algorithm is applied that converges almost surely and in mean square to a solution of the problem for any matrices $A$ and $b$ and any initial conditions of agents’ states. The algorithm is a totally asynchronous algorithm without requiring a priori B-connectivity and distribution dependency assumptions. The algorithm is able to solve the problem even if the weighted matrix of the graph is periodic and irreducible for synchronous protocol. It is demonstrated that the limit point to which the agents’ states converge is determined by the unique solution of a convex optimization problem regardless of the distribution of random communication graphs. Finally, some numerical examples are given to show the results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|