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Diagonalization of Tensors with Circulant Structure
Department of Mathematics, Tarbiat Modares University.
Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan. (Beräkningsvetenskap)ORCID-id: 0000-0003-2281-856X
2011 (engelsk)Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 435, nr 3, s. 422-447Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2011. Vol. 435, nr 3, s. 422-447
Emneord [en]
Tensor, Diagonal tensor, Circulant structure, Discrete Fourier transform, Image blurring model, Periodic boundary conditions, Preconditioner
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-63420DOI: 10.1016/j.laa.2010.03.032ISI: 000291142900002OAI: oai:DiVA.org:liu-63420DiVA, id: diva2:379569
Merknad
Original Publication: Mansoor Rezgi and Lars Eldén, Diagonalization of Tensors with Circulant Structure, 2011, Linear Algebra and its Applications, (435), 3, 422-447. http://dx.doi.org/10.1016/j.laa.2010.03.032 Copyright: Elsevier Science B.V., Amsterdam. http://www.elsevier.com/ Tilgjengelig fra: 2010-12-17 Laget: 2010-12-17 Sist oppdatert: 2017-12-11

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