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Main Title: On best rank one approximation of tensors
Author(s): Friedland, Shmuel
Mehrmann, Volker
Pajarola, Renato
Suter, Susanne
Type: Research Paper
Abstract: In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called 'alternating singular value decomposition'. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating iterations will always converge to a semi-maximal point. Finally, we introduce a new simple Newton-type method for speeding up the convergence of alternating methods near the optimum. We present several numerical examples that illustrate the computational performance of the new method in comparison to the alternating least square method.
Subject(s): singular value decomposition
rank one approximation
alternating least squares
Newton's method
Issue Date: 10-Jan-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor products
65D15 Algorithms for functional approximation
65H10 Systems of equations
65K05 Mathematical programming methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 07
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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