On Kemeny's constant and stochastic complement

Given a stochastic matrix P partitioned in four blocks Pij, i,j=1,2, Kemeny's constant κ(P) is expressed in terms of Kemeny's constants of the stochastic complements P1=P11+P12(I−P22)−1P21, and P2=P22+P21(I−P11)−1P12. Specific cases concerning periodic Markov chains and Kronecker products...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Linear algebra and its applications Ročník 703; s. 137 - 162
Hlavní autori:	Bini, Dario Andrea, Durastante, Fabio, Kim, Sooyeong, Meini, Beatrice
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 15.12.2024
Predmet:	Divide-and-conquer algorithm Kemeny's constant Markov chains 65F15 Markov chains 65C40 Kemeny's constant Divide-and-conquer algorithm 60J22
ISSN:	0024-3795
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Popis
Shrnutí:	Given a stochastic matrix P partitioned in four blocks Pij, i,j=1,2, Kemeny's constant κ(P) is expressed in terms of Kemeny's constants of the stochastic complements P1=P11+P12(I−P22)−1P21, and P2=P22+P21(I−P11)−1P12. Specific cases concerning periodic Markov chains and Kronecker products of stochastic matrices are investigated. Bounds to Kemeny's constant of perturbed matrices are given. Relying on these theoretical results, a divide-and-conquer algorithm for the efficient computation of Kemeny's constant of graphs is designed. Numerical experiments performed on real world problems show the high efficiency and reliability of this algorithm. •Expression of Kemeny's constant employing the constants of stochastic complements.•New recursive algorithms for computing Kemeny's constant.•Application of the new expression to structured transition matrices.
ISSN:	0024-3795
DOI:	10.1016/j.laa.2024.09.001