The average number of critical rank-one approximations to a tensor

Draisma, Jan; Horobet, Emil (2016). The average number of critical rank-one approximations to a tensor. Linear and multilinear algebra, 64(12), pp. 2498-2518. Taylor & Francis 10.1080/03081087.2016.1164660

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Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function to a general tensor v. As this count depends on v, we average over v drawn from a Gaussian distribution, and find formulas that relates this average to problems in random matrix theory.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Draisma, Jan

Subjects:

500 Science > 510 Mathematics

ISSN:

0308-1087

Publisher:

Taylor & Francis

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

31 Jul 2017 15:08

Last Modified:

11 Sep 2017 17:41

Publisher DOI:

10.1080/03081087.2016.1164660

ArXiv ID:

1408.3507v2

BORIS DOI:

10.7892/boris.99754

URI:

https://boris.unibe.ch/id/eprint/99754

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