On minimal subspaces in tensor representations
type: Item
instance of: scholarly article
title: On minimal subspaces in tensor representations
zbMATH Open document ID: 1260.15040
author: Antonio Falcó
author: Wolfgang Hackbusch
published in: Foundations of Computational Mathematics
publication date: 2013-01-03T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/150486
review text: There has recently been an increased interest in numerical methods which make use of tensors. Two families of applications using tensor decompositions are in the extraction and in the compression of information from complex data. Tensor product approximations are also being increasingly used in numerical analysis for the solution of problems defined in high-dimensional tensor spaces, such as certain PDEs. The authors introduce the concept of a minimal subspace of an algebraic tensor and describe a characterization. Minimal subspaces are defined and characterized for Banach tensor spaces and are used to prove the existence of a best approximation for any element in a Banach tensor space with a norm stronger than the injective norm. Examples using topological tensor products of standard Sobolev spaces are given.
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46A32
zbMATH DE Number: 6121322
zbMATH Keywords: numerical tensor calculus
zbMATH Keywords: tensor product
zbMATH Keywords: tensor Banach space
zbMATH Keywords: minimal subspace
zbMATH Keywords: weak closedness
reviewed by: Rabe von Randow
MaRDI profile type: Publication
OpenAlex ID: W2088739747
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DOI: 10.1007/S10208-012-9136-6
description: scientific article; zbMATH DE number 6121322