A Distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks

Seyyed Shaho Alaviani, Nicola Elia

Research output: Contribution to journalArticlepeer-review


This paper considers the problem of solving linear algebraic equations of the form Ax=b among multi agents 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 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 co

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
StateAccepted/In press - 2020

Bibliographical note

Publisher Copyright:


  • Convex functions
  • Distributed algorithms
  • Hilbert space
  • Mathematical model
  • Network topology
  • Protocols
  • Topology
  • asynchronous
  • distributed algorithm
  • linear algebraic equations
  • random graphs

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