Mean first passage times are an essential ingredient in both the theory and the applications of Markov chains. In the literature, they have been expressed in elegant closed-form formulas. These formulas involve explicit full matrix inversions and, if computed directly, may incur numerical instability. In this paper, we present a new iterative algorithm for computing mean first passage times in a manner that does not rely on explicit full matrix inversions. Results regarding the convergence behavior of this algorithm are also developed.
%0 Journal Article
%1 xu2015iterative
%A Xu, Jianhong
%D 2015
%J Applied Mathematics and Computation
%K Markov_chain hitting_times matrix_inverse methods
%P 372 - 389
%R https://doi.org/10.1016/j.amc.2014.11.001
%T An iterative algorithm for computing mean first passage times of Markov chains
%U http://www.sciencedirect.com/science/article/pii/S0096300314015069
%V 250
%X Mean first passage times are an essential ingredient in both the theory and the applications of Markov chains. In the literature, they have been expressed in elegant closed-form formulas. These formulas involve explicit full matrix inversions and, if computed directly, may incur numerical instability. In this paper, we present a new iterative algorithm for computing mean first passage times in a manner that does not rely on explicit full matrix inversions. Results regarding the convergence behavior of this algorithm are also developed.
@article{xu2015iterative,
abstract = {Mean first passage times are an essential ingredient in both the theory and the applications of Markov chains. In the literature, they have been expressed in elegant closed-form formulas. These formulas involve explicit full matrix inversions and, if computed directly, may incur numerical instability. In this paper, we present a new iterative algorithm for computing mean first passage times in a manner that does not rely on explicit full matrix inversions. Results regarding the convergence behavior of this algorithm are also developed.},
added-at = {2020-07-20T18:27:33.000+0200},
author = {Xu, Jianhong},
biburl = {https://www.bibsonomy.org/bibtex/26594bdcec4c6216a22688c24cb27da4a/peter.ralph},
doi = {https://doi.org/10.1016/j.amc.2014.11.001},
interhash = {9cbf87e133a5dd1c6755d28b52a1290c},
intrahash = {6594bdcec4c6216a22688c24cb27da4a},
issn = {0096-3003},
journal = {Applied Mathematics and Computation},
keywords = {Markov_chain hitting_times matrix_inverse methods},
pages = {372 - 389},
timestamp = {2020-07-20T18:27:33.000+0200},
title = {An iterative algorithm for computing mean first passage times of {Markov} chains},
url = {http://www.sciencedirect.com/science/article/pii/S0096300314015069},
volume = 250,
year = 2015
}