News Algorithms for tensor decomposition based on a reduced functional | Zendy

Kindermann Stefan | Zendy; Navasca Carmeliza | Zendy

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News Algorithms for tensor decomposition based on a reduced functional

Author(s) -

Kindermann Stefan,

Navasca Carmeliza

Publication year - 2014

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.1875

Subject(s) - mathematics , rank (graph theory) , tensor (intrinsic definition) , projection (relational algebra) , computation , rayleigh quotient , algorithm , centroid , quotient , matrix (chemical analysis) , decomposition , combinatorics , pure mathematics , eigenvalues and eigenvectors , geometry , ecology , physics , quantum mechanics , biology , materials science , composite material

SUMMARY We study the least squares functional of the canonical polyadic tensor decomposition for third order tensors by eliminating one factor matrix, which leads to a reduced functional. An analysis of the reduced functional leads to several equivalent optimization problem, such as a Rayleigh quotient or a projection. These formulations are the basis of several new algorithms as follows: the Centroid Projection method for efficient computation of suboptimal solutions and fixed‐point iteration methods for approximating the best rank‐1 and the best rank‐ R decompositions under certain nondegeneracy conditions. Copyright © 2013 John Wiley & Sons, Ltd.

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