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arXiv · 1502.03158

A Fast Distributed Solver for Symmetric Diagonally Dominant Linear Equations

Rasul Tutunov·Haitham Bou Ammar·Ali Jadbabaie
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Abstract

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 $\mathbb{G}$, the proposed distributed algorithm is capable of attaining $ε$-close solutions (for arbitrary $ε$) in time proportional to $n^{3}$ (number of nodes in $\mathbb{G}$), $α$ (upper bound on the size of the R-Hop neighborhood), and $\frac{{W}_{max}}{{W}_{min}}$ (maximum and minimum weight of edges in $\mathbb{G}$).

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Rasul Tutunov, Haitham Bou Ammar, Ali Jadbabaie. 2015-02-11. A Fast Distributed Solver for Symmetric Diagonally Dominant Linear Equations. https://arxiv.org/abs/1502.03158

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