Separation of variables for function generated high-order tensors
type: Item
instance of: scholarly article
title: Separation of variables for function generated high-order tensors
zbMATH Open document ID: 1307.65052
author: Mario Bebendorf
author: C. Kuske
published in: Journal of Scientific Computing
publication date: 2014-11-25T00:00:00Z
review text: The authors employ the previous ideas by \textit{M. Bebendorf} [Constr. Approx. 34, No. 2, 149--179 (2011; Zbl 1248.41049)] for extending adaptive cross approximation (ACA) to multivariate ACA. They separate the set of dimensions into two clusters, and repeat the procedure until the 2-way ACA method can be applied. The recursive subdivision of the set of dimensions yields a hierarchical structure, which differs from the PARATREE format.
reviewed by: Constantin Popa
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 6373690
zbMATH Keywords: adaptive cross approximation
zbMATH Keywords: tensor decomposition
zbMATH Keywords: dimension clustering
zbMATH Keywords: recursive subdivision
describes a project that uses: Algorithm 862
MaRDI profile type: Publication
full work available at URL: s10915-014-9822-4
OpenAlex ID: W2095210482
cites work: Algorithm 862
cites work: Black box approximation of tensors in hierarchical Tucker format
cites work: Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
cites work: Approximation of boundary element matrices
cites work: Adaptive cross approximation of multivariate functions
cites work: An equi-directional generalization of adaptive cross approximation for higher-order tensors
cites work: On the efficient computation of high-dimensional integrals and the approximation by exponential sums
cites work: Approximation of 1/x by exponential sums in [1, ∞)
cites work: Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young'' decomposition
cites work: Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
cites work: A theory of pseudoskeleton approximations
cites work: The maximal-volume concept in approximation by low-rank matrices
cites work: Hierarchical Singular Value Decomposition of Tensors
cites work: A new scheme for the tensor representation
cites work: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
cites work: An approach to n-mode components analysis
cites work: An Efficient Heuristic Procedure for Partitioning Graphs
cites work: A Counterexample to the Possibility of an Extension of the Eckart--Young Low-Rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition
cites work: A Multilinear Singular Value Decomposition
cites work: On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
cites work: Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
cites work: TT-cross approximation for multidimensional arrays
cites work: Sequential Unfolding SVD for Tensors With Applications in Array Signal Processing
DOI: 10.1007/S10915-014-9822-4
description: scientific article; zbMATH DE number 6373690