A Fast Distributed Solver for Symmetric Diagonally Dominant Linear Equations

In this paper, we propose a fast distributed solver for linear equations given by symmetric diagonally dominant M-Matrices. Our approach is based on a distributed implementation of the parallel solver of Spielman and Peng by considering a specific approximated inverse chain which can be computed efficiently in a distributed fashion. Representing the system of equations by a graph G, the proposed distributed algorithm is capable of attaining ǫ-close solutions (for arbitrary ǫ) in time propotional to n3 (number of nodes in G), α (upper bound on the size of the R-Hop neighborhood), and Wmax Wmin (maximum and minimum weights of edges in G). Preprint submitted to Elsevier February 12, 2015