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Perturbation Theory and Optimality Conditions for the Best Multilinear Rank Approximation of a Tensor
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0003-2281-856X
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-1542-2690
2011 (engelsk)Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 32, nr 4, s. 1422-1450Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The problem of computing the best rank-(p,q,r) approximation of a third order tensor is considered. First the problem is reformulated as a maximization problem on a product of three Grassmann manifolds. Then expressions for the gradient and the Hessian are derived in a local coordinate system at a stationary point, and conditions for a local maximum are given. A first order perturbation analysis is performed using the Grassmann manifold framework. The analysis is illustrated in a few examples, and it is shown that the perturbation theory for the singular value decomposition is a special case of the tensor theory.

sted, utgiver, år, opplag, sider
SIAM , 2011. Vol. 32, nr 4, s. 1422-1450
Emneord [en]
tensor, multilinear rank, best rank-(p, q, r) approximation, perturbation theory, first order optimality conditions, second order optimality conditions, Grassmann manifold, stationary point
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Identifikatorer
URN: urn:nbn:se:liu:diva-72910DOI: 10.1137/110823298ISI: 000298373400017OAI: oai:DiVA.org:liu-72910DiVA, id: diva2:463582
Merknad
funding agencies|Swedish Research Council||Institute for Computational Engineering and Sciences at The University of Texas at Austin||| Dnr 2008-7145 |Tilgjengelig fra: 2011-12-16 Laget: 2011-12-09 Sist oppdatert: 2017-12-08bibliografisk kontrollert

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