liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1542-2690
University of California Berkeley.
2010 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, Vol. 32, no 6, 3352-3393 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmannians or a product of Grassmannians. Specifically we defined BFGS and limited memory BFGS updates in local and global coordinates on Grassmannians or a product of these. We proved that, when local coordinates are used, our BFGS updates on Grassmannians share the same optimality property as the usual BFGS updates on Euclidean spaces. When applied to the best multilinear rank approximation problem for general and symmetric tensors, our approach yields fast, robust, and accurate algorithms that exploit the special Grassmannian structure of the respective problems and which work on tensors of large dimensions and arbitrarily high order. Extensive numerical experiments are included to substantiate our claims.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics , 2010. Vol. 32, no 6, 3352-3393 p.
Keyword [en]
Grassmann manifold, Grassmannian, product of Grassmannians, Grassmann quasi-Newton, Grassmann BFGS, Grassmann limited memory BFGS, multilinear rank, symmetric multilinear rank, tensor, symmetric tensor, approximations
National Category
URN: urn:nbn:se:liu:diva-64571DOI: 10.1137/090763172ISI: 000285551800009OAI: diva2:392814
Available from: 2011-01-28 Created: 2011-01-28 Last updated: 2013-10-11

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Savas, Berkant
By organisation
Scientific ComputingThe Institute of Technology

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 330 hits
ReferencesLink to record
Permanent link

Direct link