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 burdenâ€¦sometimes cracking problems with 10^{100} 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 [5,12] and statistics [2], stochastic dynamical systems (Fokker-Planck [21,19], and master [6,11,13] equations), quantum modelling (Schroedinger [15,14] and Liouville-von Neumann [18] equations). Surely, the numerical efficiency depends on all components of the scheme. Sometimes we also needed to develop a better preconditioner [24,9]. The tensor product formalism is also applicable to some nonlinear problems [8, 17, 3].

More details below are structured in the following categories