The tensor product methodology is one of data compression approaches in mathematical modelling, based mainly on linear algebra. Tensor decompositions offer potentially a significant reduction of the computational burden…sometimes cracking problems with 10100 or more unknowns that seem otherwise unsolvable. However, as many data-driven techniques, tensor methods are only good if the application under consideration allows that. We found positive examples in uncertainty quantification [7,16] and statistics [4], stochastic dynamical systems (Fokker-Planck [25,23], and master [8,15,17] equations), quantum modelling (Schroedinger [19,18] and Liouville-von Neumann [22] equations). Surely, the numerical efficiency depends on all components of the scheme. Sometimes we also needed to develop a better preconditioner [28,13]. The tensor product formalism is also applicable to some nonlinear problems [12, 21, 5].

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