QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images
type: Item
instance of: scholarly article
title: QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images
zbMATH Open document ID: 1244.65253
published in: Linear Algebra and its Applications
publication date: 2012-05-14T00:00:00Z
review text: The class of rank-one vectors with rank-one Fourier images is described. Also an example of a rank-one vector that has full-rank Fourier image is given. This shows that the Fourier transform is a nontrivial operation that can increase quantics tensor train (QTT) ranks of a vector to the maximum. Finally, by numerical experiments the author shows that practical \(\varepsilon\)-ranks of Fourier images of certain rank-one vectors (including the randomly distributed vectors) are moderate even for vectors of very large mode sizes.
reviewed by: S. F. Lukomskii
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 6034450
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: quantum Fourier transform
zbMATH Keywords: quantics tensor train
zbMATH Keywords: data-sparse formats
zbMATH Keywords: rank-one vectors
zbMATH Keywords: full-rank Fourier image
zbMATH Keywords: numerical experiments
author: D. V. Savostyanov
MaRDI profile type: Publication
full work available at URL: j.laa.2011.11.008
OpenAlex ID: W2020084487
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DOI: 10.1016/J.LAA.2011.11.008
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description: scientific article; zbMATH DE number 6034450