对称对角占优线性方程组的快速分布式求解器
A Fast Distributed Solver for Symmetric Diagonally Dominant Linear Equations
摘要：
本文提出了一种求解对称对角占优M-矩阵线性方程组的快速分布式算法。我们的方法是基于Spielman和彭的并行求解器的分布式实现，通过考虑一个特定的近似逆链，可以有效地计算在一个分布式的方式。表示方程组的图形$\mathbb{G}$，所提出的分布式算法是能够获得$ε$ -关闭的解决方案（对于任意$ε$）在时间上成比例的$n^{3}$（$\mathbb{G}$中的节点数），$α$（上界的R-跳邻域的大小），和$\frac{{W}_{max}}{{W}_{min}}$（最大和最小的边的重量在$\mathbb{G}$）。
英文摘要：
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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