Matthias Bolten,
Karsten Kahl,
Daniel Kressner,
Francisco Macedo,
Sonja Sokolović
S. 348 - 361
doi:
10.1553/etna_vol48s348
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol48s348
Abstract:
Markov chains that describe interacting subsystems suffer from state space explosion but lead to highly structured matrices. In this work, we propose a novel tensor-based algorithm to address such tensor-structured Markov chains. Our algorithm combines a tensorized multigrid method with AMEn, an optimization-based low-rank tensor solver, for addressing coarse grid problems. Numerical experiments demonstrate that this combination overcomes the limitations incurred when using each of the two methods individually. As a consequence, Markov chain models of unprecedented size from a variety of applications can be addressed.
Multigrid method, SVD, Tensor Train format, Markov chains, singular linear system, alternating optimization
Published Online:
2018/10/09 10:37:21
Object Identifier:
0xc1aa5576 0x0039f66f
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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