Bolten, MatthiasKahl, KarstenKressner, DanielMacedo, FranciscoSokolovic, Sonja2019-06-182019-06-182019-06-182018-01-0110.1553/etna_vol48s348https://infoscience.epfl.ch/handle/20.500.14299/157402WOS:000459295400018Markov 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.Mathematics, AppliedMathematicsmultigrid methodsvdtensor train formatmarkov chainssingular linear systemalternating optimizationlinear-systemsproducttext::journal::journal article::research article