Related papers: A Distributed Algorithm for Solving a Linear Algeb…
In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form $Ax = b$ assuming that the equation has at least one solution. The equation is presumed to be solved by $m$ agents assuming that each…
In this paper, we consider 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…
A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive…
This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than…
The paper develops a technique for solving a linear equation $Ax=b$ with a square and nonsingular matrix $A$, using a decentralized gradient algorithm. In the language of control theory, there are $n$ agents, each storing at time $t$ an…
We present a distributed asynchronous algorithm for approximating a single component of the solution to a system of linear equations $Ax = b$, where $A$ is a positive definite real matrix, and $b \in \mathbb{R}^n$. This is equivalent to…
We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network,…
This paper investigates the distributed computation of the well-known linear matrix equation in the form of $AXB = F$, with the matrices A, B, X, and F of appropriate dimensions, over multi-agent networks from an optimization perspective.…
In this work, we propose a novel discrete-time distributed algorithm for finding least-squares solutions of linear algebraic equations with a scheduling protocol to further enhance its scalability. Each agent in the network is assumed to…
This paper designs a distributed least square solution method for a linear algebraic equation over a multiagent network. The coefficient matrix is divided into multiple blocks, and each agent only knows a subset of these blocks. The…
This paper proposes distributed algorithms for multi-agent networks to achieve a solution in finite time to a linear equation $Ax=b$ where $A$ has full row rank, and with the minimum $l_1$-norm in the underdetermined case (where $A$ has…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
In this paper, a distributed subgradient-based algorithm is proposed for continuous-time multi-agent systems to search a feasible solution to convex inequalities. The algorithm involves each agent achieving a state constrained by its own…
Recently a distributed algorithm has been proposed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update…
A distributed algorithm is described for finding a common fixed point of a family of $m>1$ nonlinear maps $M_i : \mathbb{R}^n \rightarrow \mathbb{R}^n$ assuming that each map is a paracontraction and that such a common fixed point exists.…
This paper deals with linear algebraic equations where the global coefficient matrix and constant vector are given respectively, by the summation of the coefficient matrices and constant vectors of the individual agents. Our approach is…
This paper proposes a double-layered framework (or form of network) to integrate two mechanisms, termed consensus and conservation, achieving distributed solution of a linear equation. The multi-agent framework considered in the paper is…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
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…
This papers studies multi-agent (convex and \emph{nonconvex}) optimization over static digraphs. We propose a general distributed \emph{asynchronous} algorithmic framework whereby i) agents can update their local variables as well as…