Constructive Representation of Functions in Low-Rank Tensor Formats

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Only in exceptional cases, it will be possible to represent f exactly by such a sum, see [26,195,208].”
Variational quantum algorithms for nonlinear problems (2019, background): “In the case of Fourier series of order J , the approximate potential is represented by an MPS of bond dimension χ = J [51,52].”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, background): “Moreover, wide classes of functions formed by products and/or sums of trigonometric, polynomial and rational functions can be quantized in this way to yield (approximate) low-rank tensor train (TT) network formats [Khoromskij, 2011a,b, Oseledets, 2012].”