Kirkland, Steve (2010) Column Sums and the Conditioning of the Stationary Distribution for a Stochastic Matrix. Operators and Matrices, 4. pp. 431-443. ISSN 1846-3886

Download (156kB)

Abstract

For an irreducible stochastic matrix T, we consider a certain condition number (T), which measures the sensitivity of the stationary distribution vector to perturbations in T, and study the extent to which the column sum vector for T provides information on (T). Specifically, if cT is the column sum vector for some stochastic matrix of order n, we define the set S(c) = {A|A is an n × n stochastic matrix with column sum vector cT }. We then characterise those vectors cT such that (T) is bounded as T ranges over the irreducible matrices in S(c); for those column sum vectors cT for which  is bounded, we give an upper bound on  in terms of the entries in cT , and characterise the equality case.

Item Type:	Article
Keywords:	Stochastic matrix; Stationary distribution; Condition number;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	2194
Depositing User:	Professor Steve Kirkland
Date Deposited:	15 Oct 2010 11:07
Journal or Publication Title:	Operators and Matrices
Publisher:	Elements d.o.o. Publishing House
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

Repository Staff Only(login required)

Item control page

Downloads

Origin of downloads