论文标题
求解线性代数方程系统的分布式固定点方法
Distributed Fixed Point Method for Solving Systems of Linear Algebraic Equations
论文作者
论文摘要
我们提出了一类迭代完全分布的固定点方法来求解线性方程系统，以便网络中的每个代理都包含系统的方程之一。在一个通用的，强烈的连接网络下，我们证明了类似于经典，集中式，框架中的固定点方法的收敛结果：所提出的方法以线性速率收敛到线性方程系统的解决方案。我们进一步根据线性系统和网络参数明确量化了速率。接下来，我们表明该算法在随着时变的有向网络下可行的工作，只要基础图在有限的迭代间隔内连接，并且我们也为此设置建立了线性收敛速率。提出了一组数值结果，证明了该方法比现有替代方案的实际好处。
We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network, we prove a convergence result analogous to the one for fixed point methods in the classical, centralized, framework: the proposed method converges to the solution of the system of linear equations at a linear rate. We further explicitly quantify the rate in terms of the linear system and the network parameters. Next, we show that the algorithm provably works under time-varying directed networks provided that the underlying graph is connected over bounded iteration intervals, and we establish a linear convergence rate for this setting as well. A set of numerical results is presented, demonstrating practical benefits of the method over existing alternatives.
