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Title: 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 large-scale 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 multi-agent setting that accords with the distributed nature of networked systems. Distributed algorithms decompose the entire problem into many sub-problems 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 discrete-time and continuous-time algorithms. Then we will discuss the extended algorithms to achieve communication efficiency. Furthermore, we will also introduce distributed algorithms to obtain the minimum-norm solution for a system of linear equations with multiple solutions, as well as the least-squares solutions when there is no solution. Finally, themore » relationship of distributed algorithms for solving a system of linear equations to the existing distributed optimization algorithms is discussed.« less

Authors:
ORCiD logo [1];  [2];  [1];  [3]
  1. BATTELLE (PACIFIC NW LAB)
  2. Purdue University
  3. 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):
PNNL-SA-141094
DOE Contract Number:  
AC05-76RL01830
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 large-scale 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 multi-agent setting that accords with the distributed nature of networked systems. Distributed algorithms decompose the entire problem into many sub-problems 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 discrete-time and continuous-time algorithms. Then we will discuss the extended algorithms to achieve communication efficiency. Furthermore, we will also introduce distributed algorithms to obtain the minimum-norm solution for a system of linear equations with multiple solutions, as well as the least-squares 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}
}