Further discussions on a distributed algorithm for solving linear algebra equations

Abstract

In [2], a distributed algorithm has recently been developed for solving linear algebraic equations via multi-agent networks. To adopt the algorithm, each agent only has to know part of the linear equation as well as its nearby neighbors' estimates to the solution. In this paper, we would like to further discuss this algorithm from the following two perspectives. The first one is to improve the numerical stability of the algorithm and meanwhile eliminate initialization step that is necessary in [2]. The second one is to achieve a specific solution with minimum l2 norm when the linear equation has more than one solutions.