DECENTRALIZED GRADIENT ALGORITHM FOR SOLUTION OF A LINEAR EQUATION

被引：65

作者：

Anderson, Brian D. O. ^{[1
]}

Mou, Shaoshuai ^{[2
]}

Morse, A. Stephen ^{[3
]}

Helmke, Uwe ^{[4
]}

机构：

[1] Australian Natl Univ, Coll Engn & Comp Sci, Canberra, ACT, Australia

[2] Purdue Univ, Sch Aeronaut & Astronaut, W Lafayette, IN 47907 USA

[3] Yale Univ, Dept Elect Engn, New Haven, CT USA

[4] Univ Wurzburg, Dept Math, Wurzburg, Germany

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2016年 / 6卷 / 03期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

Autonomous systems; distributed algorithms; linear equations;

D O I：

10.3934/naco.2016014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper develops a technique for solving a linear equation Ax = b with a square and nonsingular matrix A, using a decentralized gradient algorithm. In the language of control theory, there are n agents, each storing at time t an n-vector, call it xi(t), and a graphical structure associating with each agent a vertex of a fixed, undirected and connected but otherwise arbitrary graph g with vertex set and edge set V and E respectively. We provide differential equation update laws for the x, with the property that each x, converges to the solution of the linear equation exponentially fast. The equation for xi includes additive terms weighting those x3 for which vertices in g corresponding to the i-th and j-th agents are adjacent. The results are extended to the case where A is not square but has full row rank, and bounds are given on the convergence rate.

引用

页码：319 / 328

页数：10

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