Compact representation of solution vectors in Kronecker-based Markovian analysis
Orhan, M. Can
QEST: International Conference on Quantitative Evaluation of Systems -13th International Conference, QEST 2016
260 - 276
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It is well known that the infinitesimal generator underlying a multi-dimensional Markov chain with a relatively large reachable state space can be represented compactly on a computer in the form of a block matrix in which each nonzero block is expressed as a sum of Kronecker products of smaller matrices. Nevertheless, solution vectors used in the analysis of such Kronecker-based Markovian representations still require memory proportional to the size of the reachable state space, and this becomes a bigger problem as the number of dimensions increases. The current paper shows that it is possible to use the hierarchical Tucker decomposition (HTD) to store the solution vectors during Kroneckerbased Markovian analysis relatively compactly and still carry out the basic operation of vector-matrix multiplication in Kronecker form relatively efficiently. Numerical experiments on two different problems of varying sizes indicate that larger memory savings are obtained with the HTD approach as the number of dimensions increases. © Springer International Publishing Switzerland 2016.
Hierarchical Tucker decomposition
Reachable state space
Multi-dimensional Markov chains
Published Version (Please cite this version)http://dx.doi.org/10.1007/978-3-319-43425-4_18
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