Approximation of Two-Variate Functions: Singular Value Decomposition Versus Regular Sparse Grids

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Based on results by Temlyakov [243–245] on bilinear approximation rates, singular value estimates for the hierarchical Tucker decomposition of functions in mixed Sobolev spaces have been obtained in [234], see also [106].”
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Harbrecht [31] argumentieren allerdings zurecht, dass in der Praxis gegenüber den linearen Methoden auch der zusätzliche Aufwand entsteht, die zunächst unbekannten Funktionen in der Schmidtzerlegung zu speichern (bzw.”
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “In [67] it was shown that when assuming only Sobolev regularity, the singular value decomposition of a bivariate function does not necessarily yield a more efficient approximation in terms of total number of coefficients than a sparse grid approximation.”