Eigenvalue invariance of inhomogeneous matrix products in distributed algorithms

Shaoshuai Mou; Brian Anderson

Eigenvalue invariance of inhomogeneous matrix products in distributed algorithms

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

Abstract

This paper establishes a general theorem concerning the eigenvalue invariance of certain inhomogeneous matrix products with respect to changes of individual multiplicands orderings. Instead of detailed entries, it is the zero-nonzero structure that matters in determining such eigenvalue invariance. The theorem is then applied in analyzing the convergence rate of a distributed algorithm for solving linear equations over networks modelled by undirected graphs.

Original language	English
Title of host publication	Proceedings, 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
Place of Publication	online
Publisher	IEEE
Pages	1030-1035
ISBN (Print)	978-1-5090-2873-3
Publication status	Published - 2017
Event	2017 56th IEEE Conference on Decision and Control (CDC) - Melbourne, Australia, Australia Duration: 1 Jan 2017 → …

Conference

Conference	2017 56th IEEE Conference on Decision and Control (CDC)
Country/Territory	Australia
Period	1/01/17 → …
Other	December 12-15,2017

Cite this

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title = "Eigenvalue invariance of inhomogeneous matrix products in distributed algorithms",

abstract = "This paper establishes a general theorem concerning the eigenvalue invariance of certain inhomogeneous matrix products with respect to changes of individual multiplicands orderings. Instead of detailed entries, it is the zero-nonzero structure that matters in determining such eigenvalue invariance. The theorem is then applied in analyzing the convergence rate of a distributed algorithm for solving linear equations over networks modelled by undirected graphs.",

author = "Shaoshuai Mou and Brian Anderson",

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AB - This paper establishes a general theorem concerning the eigenvalue invariance of certain inhomogeneous matrix products with respect to changes of individual multiplicands orderings. Instead of detailed entries, it is the zero-nonzero structure that matters in determining such eigenvalue invariance. The theorem is then applied in analyzing the convergence rate of a distributed algorithm for solving linear equations over networks modelled by undirected graphs.

M3 - Conference contribution

SN - 978-1-5090-2873-3

SP - 1030

EP - 1035

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

PB - IEEE

CY - online

T2 - 2017 56th IEEE Conference on Decision and Control (CDC)

Y2 - 1 January 2017

ER -

Eigenvalue invariance of inhomogeneous matrix products in distributed algorithms

Abstract

Conference

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