부산대학교 도서관

In this paper the authors propose a distributed algorithm on a multi-agentnetwork for solving linear systemsof algebraic equations. As agents in a network areusually separated from each other and can only communicate with theirnearby neighbors, it is natural to decompose the linear system ofequations into smaller ones and then consider how to solve the smallerones with only the information provided by the neighbor agents.\parIn this paper, for both time-invariant neighbor graphs (in subsection4.1) and time-varying neighbor graphs (in subsection 4.2), under properassumptions on the neighbor graph, by suitably updating the solution of thesmall linear systems of equations, it is shown that the globalsystem converges exponentially fast; see equation (12) in the paper and Theorem1 and Theorem 2for details. Such a conclusion is quite strong and surprising. Theupdating strategy in (12) (with $v_i$ given by (11)) plays the centralrole in the algorithm and perhaps deserves more attention.\parThe algorithm is then applied to a least squares solution problemand a network localization problem. If it had been supported by numericalexamples, theconclusion would have sounded more convincing.\parIt is noted by the authors that more attention should be paid tosolving linear systems of equations whose solutions are not unique.\par\{For further information pertaining to this item see [S. Mou et al.,Systems Control Lett. {\bf 95} (2016), 46--52; MR3514360].\}