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Analysis of 2 x 2 x 2 Tensors
Linköping University, Department of Mathematics.
2010 (English)Independent thesis Advanced level (degree of Master (Two Years)), 30 credits / 45 HE creditsStudent thesis
Abstract [en]

The question about how to determine the rank of a tensor has been widely studied in the literature. However the analytical methods to compute the decomposition of tensors have not been so much developed even for low-rank tensors.

In this report we present analytical methods for finding real and complex PARAFAC decompositions of 2 x 2 x 2 tensors before computing the actual rank of the tensor.

These methods are also implemented in MATLAB.

We also consider the question of how best lower-rank approximation gives rise to problems of degeneracy, and give some analytical explanations for these issues.

Place, publisher, year, edition, pages
2010. , 115 p.
Keyword [en]
Tensor decomposition. PARAFAC decomposition. Alternating Least Squares. Tensor Rank. Typical and generic rank. Best lower-rank approximation. Tensor Toolbox for MATLAB. Degeneracy. Uniqueness. Tensor classification.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-56762ISRN: LiTH-MAT-INT-A--2010/01--SEOAI: oai:DiVA.org:liu-56762DiVA: diva2:321908
Presentation
2010-06-01, Kompakta Rummet, B huset, Linköping, 10:00 (English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2010-06-03 Created: 2010-06-02 Last updated: 2010-10-26Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf