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Diagonalization of Tensors with Circulant Structure
Department of Mathematics, Tarbiat Modares University.
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology. (Beräkningsvetenskap)ORCID iD: 0000-0003-2281-856X
2011 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 435, no 3, 422-447 p.Article in journal (Refereed) Published
Abstract [en]

The concepts of tensors with diagonal and circulant structure are defined and aframework is developed for the analysis of such tensors. It is shown a tensor of arbitraryorder, which is circulant with respect to two particular modes, can be diagonalized inthose modes by discrete Fourier transforms. This property can be used in the efficientsolution of linear systems involving contractive products of tensors with circulantstructure. Tensors with circulant structure occur in models for image blurring withperiodic boundary conditions. It is shown that the new framework can be applied tosuch problems.

Place, publisher, year, edition, pages
2011. Vol. 435, no 3, 422-447 p.
Keyword [en]
Tensor, Diagonal tensor, Circulant structure, Discrete Fourier transform, Image blurring model, Periodic boundary conditions, Preconditioner
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-63420DOI: 10.1016/j.laa.2010.03.032ISI: 000291142900002OAI: diva2:379569
Original Publication: Mansoor Rezgi and Lars Eldén, Diagonalization of Tensors with Circulant Structure, 2011, Linear Algebra and its Applications, (435), 3, 422-447. Copyright: Elsevier Science B.V., Amsterdam. Available from: 2010-12-17 Created: 2010-12-17 Last updated: 2013-08-30

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