Premium
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.