Two-level Tucker-TT-QTT format for optimized tensor calculus

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A literature survey of low‐rank tensor approximation techniques (2013, positive): “For the following matrices, QTT representations have been discussed: Toeplitz matrices [136,216], (inverse) Laplace operators [139,205], linear diffusion operators [62,138].”
Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis (2013, background): “Further promising generalizations can be based on a combination of the Tucker, TT and QTT formats [26, 11].”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “It brings the notations in consistence with previous papers on the numerical tensor methods, e.g. [18, 9, 8, 35] and others.”
Efficient time-stepping scheme for dynamics on TT-manifolds (2012, unknown): “The approach considered in this paper can be extended to more general tensor manifolds, in particular, to the two-level Tucker-TT-QTT format [7].”
Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, methodology): “In [38] it was shown that the TT versions of these solvers can be naturally exploited inside the corresponding algorithms for the QTT-Tucker format.”