矩阵方程的分布式求解算法研究概述

In recent years, with the rise of large-scale networks and the widespread application of distributed optimization theory, distributed algorithms for solving matrix equations have received increasing research attention. The computation of matrix equations is of great importance in both theoretical and engineering fields. In the distributed computation over multi-agent networks, the data information of matrix equations is partitioned in various ways. Each agent is able to obtain only one partition of the data and communicate with its neighbors, but all the agents can cooperatively solve different types of solutions as required. In this survey, we focus on the distributed algorithms in recent matrix computation problems, such as linear algebraic equations, several types of unconstrained and constrained linear matrix equations, and other matrix-related problems. We introduce distributed algorithms such as projection with consensus, distributed optimization transformation, and special methods such as message passing methods for sparse ones. Finally, we give a brief summary and an outlook on the research area of distributed matrix computation.