# Directed forests with application to algorithms related to Markov chains

Applicationes Mathematicae (1999)

- Volume: 26, Issue: 4, page 395-414
- ISSN: 1233-7234

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topPokarowski, Piotr. "Directed forests with application to algorithms related to Markov chains." Applicationes Mathematicae 26.4 (1999): 395-414. <http://eudml.org/doc/219248>.

@article{Pokarowski1999,

abstract = {This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.},

author = {Pokarowski, Piotr},

journal = {Applicationes Mathematicae},

keywords = {entrywise relative error; directed forest; Matrix Tree Theorem; directed graph; Simulated Annealing; Markov chains; Metropolis algorithm; direct methods for linear systems; nearly completely decomposable Markov chains; aggregation algorithms; nonhomogeneous Markov chains; Markov Chain Tree Theorem; Markov chain Monte Carlo algorithms; Gibbs sampler; simulated annealing; directed forest expansions; matrix tree theorem; systems of linear equations; Markov chain Monte Carlo procedures},

language = {eng},

number = {4},

pages = {395-414},

title = {Directed forests with application to algorithms related to Markov chains},

url = {http://eudml.org/doc/219248},

volume = {26},

year = {1999},

}

TY - JOUR

AU - Pokarowski, Piotr

TI - Directed forests with application to algorithms related to Markov chains

JO - Applicationes Mathematicae

PY - 1999

VL - 26

IS - 4

SP - 395

EP - 414

AB - This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.

LA - eng

KW - entrywise relative error; directed forest; Matrix Tree Theorem; directed graph; Simulated Annealing; Markov chains; Metropolis algorithm; direct methods for linear systems; nearly completely decomposable Markov chains; aggregation algorithms; nonhomogeneous Markov chains; Markov Chain Tree Theorem; Markov chain Monte Carlo algorithms; Gibbs sampler; simulated annealing; directed forest expansions; matrix tree theorem; systems of linear equations; Markov chain Monte Carlo procedures

UR - http://eudml.org/doc/219248

ER -

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