Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High-Dimensional Elliptic Problems

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “In [93, 110, 111, 115], combinations of low-rank tensor formats with hierarchical matrices are investigated.”
MACH: Fast Randomized Tensor Decompositions (2009, background): “ grows bigger (i.e., the number of non-zeros) the speedup should become apparent. For example consider a tensor X∈Rn×n×n, with X ijk = 1 i+j+k and assume we want an (r,r,r) approximation. As shown in [16, 50] for an approximationwith error ǫthe rank grows logarithmically with n and ǫ, satisfying ine”
Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse (2012, methodology): “The TT and QTT approximations of the inverse Laplace matrix can be obtained through the quadrature techniques suggested in [14, 10, 4].”
Variational calculus with sums of elementary tensors of fixed rank (2012, unknown): “Mathematics Subject Classification 15A69 · 90C06 · 65F10”
Møller-Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals (2014, background): “for xi ≥ 0,  xi > δ, which converges exponentially fast in M , see [32,33].”
QTT approximation of elliptic solution operators in higher dimensions (2011, methodology): “We will use the the following specific approximation to the inverse [12, 13]”