Adaptive Cross Approximation of Multivariate Functions

By Mario Bebendorf. 2011

100 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “The adaptive cross approximation for the Tucker decomposition has been analyzed in [20].”
Approximation of Two-Variate Functions: Singular Value Decomposition Versus Regular Sparse Grids (2010, background): “They are a-priorily unknown and need thus to be approximated by systematic basis functions of some ansatz spaces V (1) J ⊂ L2(Ω1) and V (2) J ⊂ L2(Ω2), respectively, which is indeed the case in most practical applications.”
Approximation of bi-variate functions: singular value decomposition versus sparse grids (2014, methodology): “Related representation methods have recently been considered in Bebendorf (2011), Grasedyck (2010), Hackbusch (2012), Hackbusch &K̈uhn (2009), or Oseledets & Tyrtyshnikov (2009).”
Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances (2012, methodology): “A direct method of the Tucker decomposition for d = 3, based on the adaptive cross approximation is presented in [76, 3].”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “…to provide stable Full text available at: http://dx.doi.org/10.1561/2200000059 quasi-optimal rank reduction, achieved through, for example, truncated singular value decompositions (tSVD) or adaptive cross-approximation (Oseledets and Tyrtyshnikov, 2010; Bebendorf, 2011; Khoromskij and Veit, 2016).”
F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Generalized Cross Approximation for 3d-tensors Generalized Cross Approximation for 3d-tensors (methodology): “A natural extension of the bivariate method to functions of three or four variables is proposed in [2] and can be seen as nested ACA.”