A Kronecker product approximate preconditioner for SANs
نویسندگان
چکیده
منابع مشابه
A Kronecker product approximate preconditioner for SANs
Many very large Markov chains can be modelled e ciently as stochastic automata networks (SANs). A SAN is composed of individual automata which, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum of Kronecker products of smaller matrices. Thus, storage savings are immediate. The be...
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The discretization of linear partial differential equations with random data by means of the stochastic Galerkin finite element method results in general in a large coupled linear of system of equations. Using the stochastic diffusion equation as a model problem, we introduce and study a symmetric positive definite Kronecker product preconditioner for the Galerkin matrix. We compare the popular...
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T paper is the experimental follow-up to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a...
متن کاملPreconditioning for Stochastic Automata Networks
LANGVILLE, AMY N. Preconditioning for Stochastic Automata Networks. (Under the direction of William J. Stewart.) Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN is composed of individual automata that, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov ...
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In this paper we develop new techniques for stabilizing factored approximate inverse preconditioners (AINV) using pivoting. This method yields stable preconditioners in many cases and can provide successful preconditioners in many situations when the underlying system is highly indefinite. Numerical examples illustrate the effectiveness of this approach.
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2004
ISSN: 1070-5325,1099-1506
DOI: 10.1002/nla.344