A structured condition number for Kemeny's constant
| dc.contributor.author | Breen, Jane | |
| dc.contributor.author | Kirkland, Steve | |
| dc.date.accessioned | 2020-01-03T16:16:14Z | |
| dc.date.available | 2020-01-03T16:16:14Z | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2020-01-02T16:41:36Z | en |
| dc.description.abstract | Kemeny's constant is an interesting and useful quantifier describing the global average behaviour of a Markov chain. In this article, we examine the sensitivity of Kemeny's constant to perturbations in the transition probabilities. That is, we consider the problem of generating a condition number for Kemeny's constant, to give an indication of the size of the change in its value relative to the size of the perturbation. We provide a structured condition number and determine some illuminating upper and lower bounds which connect the conditioning of Kemeny's constant to well-studied condition numbers for the stationary vector of the Markov chain. We also investigate the behaviour of this structured condition number for several infinite families of Markov chains. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/34436 | |
| dc.language.iso | eng | en_US |
| dc.publisher | SIAM Journal on Matrix Analysis and Applications | en_US |
| dc.rights | open access | en_US |
| dc.subject | Kemeny's constant | en_US |
| dc.subject | condition number | en_US |
| dc.subject | Markov chains | en_US |
| dc.subject | group inverse | en_US |
| dc.title | A structured condition number for Kemeny's constant | en_US |
| dc.type | Article | en_US |