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A Newton-Grassmann method for computing the best multilinear rank-(r1,r2,r3) approximation of a tensorPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2009 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, Vol. 32, no 2, p. 248-271Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2009. Vol. 32, no 2, p. 248-271
##### Keywords [en]

tensor, multilinear, rank, approximation, Grassmann manifold, Newton
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-13193DOI: 10.1137/070688316OAI: oai:DiVA.org:liu-13193DiVA, id: diva2:18009
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1172",{id:"formSmash:j_idt1172",widgetVar:"widget_formSmash_j_idt1172",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1178",{id:"formSmash:j_idt1178",widgetVar:"widget_formSmash_j_idt1178",multiple:true}); Available from: 2008-04-29 Created: 2008-04-29 Last updated: 2013-10-11
##### In thesis

We^{ }derive a Newton method for computing the best rank-$(r_1,r_2,r_3)$ approximation^{ }of a given $J\times K\times L$ tensor $\mathcal{A}$. The problem^{ }is formulated as an approximation problem on a product of^{ }Grassmann manifolds. Incorporating the manifold structure into Newton's method ensures^{ }that all iterates generated by the algorithm are points on^{ }the Grassmann manifolds. We also introduce a consistent notation for^{ }matricizing a tensor, for contracted tensor products and some tensor-algebraic^{ }manipulations, which simplify the derivation of the Newton equations and^{ }enable straightforward algorithmic implementation. Experiments show a quadratic convergence rate^{ }for the Newton–Grassmann algorithm.

1. Algorithms in data mining using matrix and tensor methods$(function(){PrimeFaces.cw("OverlayPanel","overlay18011",{id:"formSmash:j_idt1464:0:j_idt1468",widgetVar:"overlay18011",target:"formSmash:j_idt1464:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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