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Quasi-Newton algorithm for best multi-linear rank approximation of tensors
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.ORCID iD: 0000-0002-1542-2690
ICME Stanford University.
2007 (English)In: 6th International Congress on Industrial and Applied Mathematics,2007, 2007Conference paper, Published paper (Other academic)
Abstract [en]

In this talk we introduce a novel method for solving the best multilinear rank approximation problem. Our algorithm differs from existing methods in two respects: (1) it exploits the fact that the problem may be viewed as an optimization problem over a product of Grassmann manifolds; (2) it uses Quasi-Newton-like Hessian-approximates specially adapted for Grassmannians and thus avoids the inevitable problem of large Hessians in such problems. Tensor approximation problems occur in various applications involving multidimensional data. The performance of the Quasi-Newton algorithm is compared with the Newton-Grassmann and Higher Order Orthogonal Iteration algorithms for general and symmetric 3-tensors.

Place, publisher, year, edition, pages
2007.
Keyword [en]
tensor approximation, multilinear rank, optimization on manifolds, product manifolds
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-40925Local ID: 54654OAI: oai:DiVA.org:liu-40925DiVA: diva2:261774
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-10-11

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Savas, Berkant

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