Subtracting a best rank‐1 approximation from  p  ×  p  × 2( p ≥2) tensors | Zendy

Kong Xu | Zendy; Jiang YaoLin | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Subtracting a best rank‐1 approximation from p × p × 2( p ≥2) tensors

Author(s) -

Kong Xu,

Jiang YaoLin

Publication year - 2012

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.780

Subject(s) - multilinear map , rank (graph theory) , mathematics , correctness , conjecture , orthonormal basis , tensor (intrinsic definition) , multilinear algebra , algebra over a field , combinatorics , pure mathematics , algorithm , quantum mechanics , physics , division algebra , filtered algebra

SUMMARY We introduce one special form of the ptimesp × 2 ( p ≥2) tensors by multilinear orthonormal transformations, and present some interesting properties of the special form. Through discussing on the special form, we provide a solution to one conjecture proposed by Stegeman and Comon in a conference paper ( Proceedings of the EUSIPCO 2009 Conference , Glasgow, Scotland, 2009), and reveal an important conclusion about subtracting a best rank‐1 approximations from p × p × 2 tensors of the special form. All of these confirm that consecutively subtracting the best rank‐1 approximations may not lead to a best low rank approximation of a tensor. Numerical examples show the correctness of our theory. Copyright © 2011 John Wiley & Sons, Ltd.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research