منابع مشابه
Smoothed Aggregation Multigrid for Markov Chains
A smoothed aggregation multigrid method is presented for the numerical calculation of the stationary probability vector of an irreducible sparse Markov chain. It is shown how smoothing the interpolation and restriction operators can dramatically increase the efficiency of aggregation multigrid methods for Markov chains that have been proposed in the literature. The proposed smoothing approach i...
متن کاملRecursively Accelerated Multilevel Aggregation for Markov Chains
A recursive acceleration method is proposed for multiplicative multilevel aggregation algorithms that calculate the stationary probability vector of large, sparse and irreducible Markov chains. Pairs of consecutive iterates at all branches and levels of a multigrid W cycle with simple, nonoverlapping aggregation are recombined to produce improved iterates at those levels. This is achieved by so...
متن کاملThe Finest Level Acceleration of Multilevel Aggregation for Markov Chains
In this paper, we consider a class of new accelerated multilevel aggregation methods using two polynomial-type vector extrapolation methods, namely the reduced rank extrapolation (RRE) and the generalization of quadratic extrapolation (GQE) methods. We show how to combine the multilevel aggregation methods with the RRE and GQE algorithms on the finest level in order to speed up the numerical co...
متن کاملHigher-Order Kullback-Leibler Aggregation of Markov Chains
In this work, we consider the problem of reducing a first-order Markov chain on a large alphabet to a higher-order Markov chain on a small alphabet. We present informationtheoretic cost functions that are related to predictability and lumpability, show relations between these cost functions, and discuss heuristics to minimize them. Our experiments suggest that the generalization to higher order...
متن کاملEmpirical Bayes Estimation in Nonstationary Markov chains
Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical Bayes estimators for the transition probability matrix of a finite nonstationary Markov chain. The data are assumed to be of a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1993
ISSN: 0304-4149
DOI: 10.1016/0304-4149(93)90062-9