Multigrid methods combined with low-rank approximation for tensor-structured Markov chains

Matthias Bolten, Karsten Kahl, Daniel Kressner, Francisco Macedo, Sonja Sokolović
2018 Electronic Transactions on Numerical Analysis  
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
more » ... ds individually. As a consequence, Markov chain models of unprecedented size from a variety of applications can be addressed.
doi:10.1553/etna_vol48s348 fatcat:hwpj4q6v4jdsjb66fo72qbdmpu