A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format
type: Item
instance of: scholarly article
title: A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format
zbMATH Open document ID: 1264.65087
author: Mike Espig
author: Wolfgang Hackbusch
published in: Numerische Mathematik
publication date: 2013-02-04T00:00:00Z
review text: In the introduction the authors ``consider a rank approximation algorithm for tensors represented in the canonical format in arbitrary pre-Hilbert tensor product spaces. It is shown that the original approximation problem is equivalent to a finite-dimensional \(l_2\) minimization problem. The \(l_2\) minimization problem is solved by a regularized Newton method which requires the computation and evaluation of the first and second derivative of the objective function. A systematic choice of the initial guess for the iterative scheme is introduced. The effectiveness of the approach is demonstrated in numerical experiments.''
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 90C06
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 6134327
zbMATH Keywords: minimization method
zbMATH Keywords: regularized Newton method
zbMATH Keywords: low tensor rank approximation
zbMATH Keywords: algorithm
zbMATH Keywords: pre-Hilbert tensor product spaces
zbMATH Keywords: numerical experiments
reviewed by: Nada Djuranović-Miličić
describes a project that uses: Multilinear Engine
MaRDI profile type: Publication
full work available at URL: s00211-012-0465-9
OpenAlex ID: W2071529930
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DOI: 10.1007/S00211-012-0465-9
description: scientific article; zbMATH DE number 6134327