Tensor structured Markov chains are part of stochastic models of manypractical applications, e.g., in the description of complex production ortelephone networks. The most interesting question in Markov chain models is thedetermination of the stationary distribution as a description of the long termbehavior of the system. This involves the computation of the eigenvectorcorresponding to the dominant eigenvalue or equivalently the solution of asingular linear system of equations. Due to the tensor structure of the modelsthe dimension of the operators grows rapidly and a direct solution withoutexploiting the tensor structure becomes infeasible. Algebraic multigrid methodshave proven to be efficient when dealing with Markov chains without usingtensor structure. In this work we present an approach to adapt the algebraicmultigrid framework to the tensor frame, not only using the tensor structure inmatrix-vector multiplications, but also tensor structured coarse-grid operatorsand tensor representations of the solution vector.
展开▼
