Network flows as least squares solvers for linear equations

Yang Liu; Youcheng Lou; Brian D.O. Anderson; Guodong Shi

doi:10.1109/CDC.2017.8263795

Network flows as least squares solvers for linear equations

Yang Liu, Youcheng Lou, Brian D.O. Anderson, Guodong Shi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

This paper presents a first-order continuous-time distributed step-size algorithm for computing the least squares solution to a linear equation over networks. Given the uniqueness of the solution and nonintegrable step size, the convergence results are provided for fixed graphs. For the nonunique solution and square integrable step size, the convergence is shown for constantly connected switching graphs. We also validate the results and illustrate possible impacts on the convergence speed using a few numerical examples.

Original language	English
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1046-1051
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8263795
Publication status	Published - 28 Jun 2017
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: 12 Dec 2017 → 15 Dec 2017

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Conference

Conference	56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 15/12/17

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10.1109/CDC.2017.8263795

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Liu, Y., Lou, Y., Anderson, B. D. O., & Shi, G. (2017). Network flows as least squares solvers for linear equations. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 1046-1051). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8263795

@inproceedings{52a4bbdd5c374296b1d3e38b9a52e126,

title = "Network flows as least squares solvers for linear equations",

abstract = "This paper presents a first-order continuous-time distributed step-size algorithm for computing the least squares solution to a linear equation over networks. Given the uniqueness of the solution and nonintegrable step size, the convergence results are provided for fixed graphs. For the nonunique solution and square integrable step size, the convergence is shown for constantly connected switching graphs. We also validate the results and illustrate possible impacts on the convergence speed using a few numerical examples.",

author = "Yang Liu and Youcheng Lou and Anderson, {Brian D.O.} and Guodong Shi",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.; 56th IEEE Annual Conference on Decision and Control, CDC 2017 ; Conference date: 12-12-2017 Through 15-12-2017",

year = "2017",

month = jun,

day = "28",

doi = "10.1109/CDC.2017.8263795",

language = "English",

series = "2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Liu, Y, Lou, Y, Anderson, BDO & Shi, G 2017, Network flows as least squares solvers for linear equations. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 1046-1051, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8263795

Network flows as least squares solvers for linear equations. / Liu, Yang; Lou, Youcheng; Anderson, Brian D.O. et al.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 1046-1051 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Network flows as least squares solvers for linear equations

AU - Liu, Yang

AU - Lou, Youcheng

AU - Anderson, Brian D.O.

AU - Shi, Guodong

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N2 - This paper presents a first-order continuous-time distributed step-size algorithm for computing the least squares solution to a linear equation over networks. Given the uniqueness of the solution and nonintegrable step size, the convergence results are provided for fixed graphs. For the nonunique solution and square integrable step size, the convergence is shown for constantly connected switching graphs. We also validate the results and illustrate possible impacts on the convergence speed using a few numerical examples.

AB - This paper presents a first-order continuous-time distributed step-size algorithm for computing the least squares solution to a linear equation over networks. Given the uniqueness of the solution and nonintegrable step size, the convergence results are provided for fixed graphs. For the nonunique solution and square integrable step size, the convergence is shown for constantly connected switching graphs. We also validate the results and illustrate possible impacts on the convergence speed using a few numerical examples.

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M3 - Conference contribution

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SP - 1046

EP - 1051

BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

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T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017

Y2 - 12 December 2017 through 15 December 2017

ER -

Network flows as least squares solvers for linear equations

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