부산대학교 도서관

In this paper the authors propose a distributed algorithm on a multi-agent network for solving linear systems of algebraic equations. As agents in a network are usually separated from each other and can only communicate with their nearby neighbors, it is natural to decompose the linear system of equations into smaller ones and then consider how to solve the smaller ones with only the information provided by the neighbor agents. \par In this paper, for both time-invariant neighbor graphs (in subsection 4.1) and time-varying neighbor graphs (in subsection 4.2), under proper assumptions on the neighbor graph, by suitably updating the solution of the small linear systems of equations, it is shown that the global system converges exponentially fast; see equation (12) in the paper and Theorem 1 and Theorem 2 for details. Such a conclusion is quite strong and surprising. The updating strategy in (12) (with $v_i$ given by (11)) plays the central role in the algorithm and perhaps deserves more attention. \par The algorithm is then applied to a least squares solution problem and a network localization problem. If it had been supported by numerical examples, the conclusion would have sounded more convincing. \par It is noted by the authors that more attention should be paid to solving 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].\}