Directed forests with application to algorithms related to Markov chains

Piotr Pokarowski

Applicationes Mathematicae (1999)

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

Abstract

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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.

How to cite

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Pokarowski, 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 -

References

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