A Fast Distributed Solver for Symmetric Diagonally Dominant Linear Equations
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 $\epsilon$-close solutions (for arbitrary $\epsilon$) in time proportional to $n^{3}$ (number of nodes in $\mathbb{G}$), ${\alpha}$ (upper bound on the size of the R-Hop neighborhood), and $\frac{{W}_{max}}{{W}_{min}}$ (maximum and minimum weight of edges in $\mathbb{G}$).
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2015
- DOI:
- 10.48550/arXiv.1502.03158
- arXiv:
- arXiv:1502.03158
- Bibcode:
- 2015arXiv150203158T
- Keywords:
-
- Computer Science - Distributed;
- Parallel;
- and Cluster Computing