Kirkland, Steve
(2010)
Column Sums and the Conditioning of the
Stationary Distribution for a Stochastic Matrix.
Operators and Matrices, 4.
pp. 431443.
ISSN 18463886
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) =
{AA 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: 

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