منابع مشابه
Algebraic Multigrid for Markov Chains
An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed that produces a nonnegative interpolation operator with unit row sums. We show how the adoption of ...
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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...
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A new adaptive algebraic multigrid scheme is developed for the solution of Markov chains, where the hierarchy of operators is adapted on-the-fly in a setup process that is interlaced with the solution process. The setup process feeds the solution process with improved operators, while the solution process provides the adaptive setup process with better approximations on which to base further-im...
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We propose several algorithms to obtain bounds based on Censored Markov Chains to analyze partially generated discrete time Markov chains. The main idea is to avoid the generation of a huge (or even infinite) state space and to truncate the state space during the visit. The approach is purely algebraic and provides element-wise and stochastic bounds for the CMC.
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This work concerns the development of an algebraic multilevel method for computing state vectors of Markov chains. We present an efficient bootstrap algebraic multigrid method for this task. In our proposed approach, we employ a multilevel eigensolver, with interpolation built using ideas based on compatible relaxation, algebraic distances, and least squares fitting of test vectors. Our adaptiv...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2010
ISSN: 1064-8275,1095-7197
DOI: 10.1137/090753589