Compact representation of solution vectors in Kronecker-based Markovian analysis
Date
2016-08Source Title
QEST: International Conference on Quantitative Evaluation of Systems -13th International Conference, QEST 2016
Print ISSN
0302-9743
Publisher
Springer
Pages
260 - 276
Language
English
Type
Conference PaperItem Usage Stats
241
views
views
487
downloads
downloads
Abstract
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.
Keywords
Compact vectorsHierarchical Tucker decomposition
Kronecker products
Markov chains
Reachable state space
Chains
Markov processes
Matrix algebra
Vectors
Compact representation
Infinitesimal generator
Kronecker product
Markovian representation
Multi-dimensional Markov chains
Numerical experiments
Tucker decompositions
Vector-matrix multiplications
Vector spaces
Permalink
http://hdl.handle.net/11693/37502Published Version (Please cite this version)
http://dx.doi.org/10.1007/978-3-319-43425-4_18Collections
Related items
Showing items related by title, author, creator and subject.
-
A tool for pattern information extraction and defect quantification from crystal structures
Okuyan, E.; Okuyan, E. (Elsevier, 2015)In this paper, we present a revised version of BilKristal 2.0 tool. We added defect quantification functionality to assess crystalline defects. We improved visualization capabilities by adding transparency support and ... -
BilKristal 4.0: A tool for crystal parameters extraction and defect quantification
Okuyan, E.; Okuyan, C. (Elsevier, 2015)In this paper, we present a revised version of BilKristal 3.0 tool. Raycast screenshot functionality is added to provide improved visual analysis. We added atomic distance analysis functionality to assess crystalline ... -
A parametric simplex algorithm for linear vector optimization problems
Rudloff, B.; Ulus, F.; Vanderbei, R. (Springer, 2017)In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans–Steuer) algorithm (Math ...