On Kemeny's constant and stochastic complement

被引：0

作者：

Bini, Dario Andrea ^{[1
]}

Durastante, Fabio ^{[1
]}

Kim, Sooyeong ^{[2
]}

Meini, Beatrice ^{[1
]}

机构：

[1] Univ Pisa, Math Dept, Largo Bruno Pontecorvo 5, I-56127 Pisa, PI, Italy

[2] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2024年 / 703卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Markov chains; Kemeny's constant; Divide-and-conquer algorithm;

D O I：

10.1016/j.laa.2024.09.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a stochastic matrix P partitioned in four blocks P-ij, i, j = 1, 2, Kemeny's constant kappa(P) is expressed in terms of Kemeny's constants of the stochastic complements P-1 = P(1)1+ P-12(I-P-22)-1P(21), and P-2 = P-22+P-21(I-P-11)-1P(12). 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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

引用

页码：137 / 162

页数：26

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