Asynchronous Stochastic Block Projection Algorithm for Solving Linear Systems under Predefined Communication Patterns

• DOI: 10.48550/arxiv.2502.14213
• Publication Date: 2025-02-19
• Authors: Yanchen Yin; Yongli Wang
• Keywords: FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA)

Distributed computation over networks is now receiving an increasing attention in many fields such as engineering and machine learning, where the solution of a linear system equations basic task. This paper presents asynchronous distributed randomized block Kaczmarz projection algorithm for solving large-scale systems multi-agent networks, each agent only holds part problem data. An event-triggered communication mechanism integrated to minimize overhead reduce overall costs. allows update independently environment dynamically regulate frequency. In addition, this article analyzes inefficiency caused by algorithms, explores potential event triggering mechanisms alleviating these problems, provides general conditions global convergence environments. Moreover, modified stochastic used their local estimate. Through rigorous mathematical analysis, exponential rate proposed established consistent its computational efficiency, robustness, efficiency validated through extensive numerical experiments. Furthermore, address inconsistent systems, introduces auxiliary variables facilitate toward approximate least-squares solution, accompanied formal error analysis. The experimental results demonstrate that maintains stability even under extreme asynchrony, failures, node while achieving significantly lower faster rates compared traditional methods.