Solving a system of linear equations: From centralized to distributed methods
Abstract
For a wide range of control engineering applications, the problem of solving a system of linear equations is often encountered and has been well studied. Traditionally, this problem has been mainly solved in a centralized manner. However, for applications related to largescale complex networked systems, centralized algorithms are often subjected to some practical issues due to limited computational power and communication bandwidth. As a promising and viable alternative, distributed algorithms can effectively address the issues associated with centralized algorithms by solving the problem efficiently in a multiagent setting that accords with the distributed nature of networked systems. Distributed algorithms decompose the entire problem into many subproblems that are solved by individual agents in a cooperative manner. In this survey paper, we provide a detailed overview of the state of the art relevant to distributed algorithms for solving a system of linear equations. We will first review basic distributed algorithms including both discretetime and continuoustime algorithms. Then we will discuss the extended algorithms to achieve communication efficiency. Furthermore, we will also introduce distributed algorithms to obtain the minimumnorm solution for a system of linear equations with multiple solutions, as well as the leastsquares solutions when there is no solution. Finally, themore »
 Authors:

 BATTELLE (PACIFIC NW LAB)
 Purdue University
 University of California, Riverside
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1547371
 Report Number(s):
 PNNLSA141094
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Journal Article
 Journal Name:
 Annual Reviews in Control
 Additional Journal Information:
 Journal Volume: 47
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Wang, Peng, Mou, Shaoshuai, Lian, Jianming, and Ren, Wei. Solving a system of linear equations: From centralized to distributed methods. United States: N. p., 2019.
Web. doi:10.1016/j.arcontrol.2019.04.008.
Wang, Peng, Mou, Shaoshuai, Lian, Jianming, & Ren, Wei. Solving a system of linear equations: From centralized to distributed methods. United States. doi:10.1016/j.arcontrol.2019.04.008.
Wang, Peng, Mou, Shaoshuai, Lian, Jianming, and Ren, Wei. Mon .
"Solving a system of linear equations: From centralized to distributed methods". United States. doi:10.1016/j.arcontrol.2019.04.008.
@article{osti_1547371,
title = {Solving a system of linear equations: From centralized to distributed methods},
author = {Wang, Peng and Mou, Shaoshuai and Lian, Jianming and Ren, Wei},
abstractNote = {For a wide range of control engineering applications, the problem of solving a system of linear equations is often encountered and has been well studied. Traditionally, this problem has been mainly solved in a centralized manner. However, for applications related to largescale complex networked systems, centralized algorithms are often subjected to some practical issues due to limited computational power and communication bandwidth. As a promising and viable alternative, distributed algorithms can effectively address the issues associated with centralized algorithms by solving the problem efficiently in a multiagent setting that accords with the distributed nature of networked systems. Distributed algorithms decompose the entire problem into many subproblems that are solved by individual agents in a cooperative manner. In this survey paper, we provide a detailed overview of the state of the art relevant to distributed algorithms for solving a system of linear equations. We will first review basic distributed algorithms including both discretetime and continuoustime algorithms. Then we will discuss the extended algorithms to achieve communication efficiency. Furthermore, we will also introduce distributed algorithms to obtain the minimumnorm solution for a system of linear equations with multiple solutions, as well as the leastsquares solutions when there is no solution. Finally, the relationship of distributed algorithms for solving a system of linear equations to the existing distributed optimization algorithms is discussed.},
doi = {10.1016/j.arcontrol.2019.04.008},
journal = {Annual Reviews in Control},
number = ,
volume = 47,
place = {United States},
year = {2019},
month = {7}
}