具有标量化压缩的网络线性方程分布式求解器
Distributed Solvers for Network Linear Equations with Scalarized Compression
AI总结：
本文研究网络线性方程的分布式求解器，提出包含压缩向量和数据展开的维度压缩方案，将节点间通信消息压缩为标量值，并基于压缩一致性流开发了连续与离散求解器，证明了其线性收敛性且有效降低了通信负担。
摘要：
分布式计算是多智能体系统的基础，其中求解分布式线性方程是一个典型例子。本文研究了网络线性方程的分布式求解器，其节点间通信消息被压缩为标量值。核心思想在于一种维度压缩方案，包含维度压缩向量和数据展开步骤。压缩向量通过内积作用于各节点状态，生成用于节点通信的实值消息。在展开步骤中，该标量消息随后沿压缩向量生成的子空间进行投影以进行局部计算。我们首先提出一种仅依赖此类标量化通信的压缩一致性流，并证明在压缩向量具有充分激励信号的情况下可实现线性收敛。随后，我们将该压缩一致性流作为基本一致性子程序，开发了网络线性方程的分布式连续时间和离散时间求解器，并证明了其在标量节点通信下的线性收敛特性。采用标量通信的直接益处是降低了分布式计算中节点间通信信道的负担。最后给出了数值示例以验证所建立理论结果的有效性。
英文摘要：
Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme that includes a dimension-compressing vector and a data unfolding step. The compression vector applies to individual node states as an inner product to generate a real-valued message for node communication. In the unfolding step, such scalar message is then plotted along the subspace generated by the compression vector for the local computations. We first present a compressed consensus flow that relies only on such scalarized communication, and show that linear convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their linear convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel burden for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
