Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation | Zendy

André Uschmajew | Zendy

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Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation

Author(s) -

André Uschmajew

Publication year - 2012

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/110843587

Subject(s) - mathematics , hessian matrix , rank (graph theory) , convergence (economics) , regularization (linguistics) , tensor (intrinsic definition) , low rank approximation , modulo , scaling , algorithm , mathematical analysis , pure mathematics , combinatorics , geometry , economics , economic growth , artificial intelligence , computer science

A local convergence theorem for calculating canonical low-rank tensor approximations (PARAFAC, CANDECOMP) by the alternating least squares algorithm is established. The main assumption is that the Hessian matrix of the problem is positive definite modulo the scaling indeterminacy. A discussion, whether this is realistic, and numerical illustrations are included. Also regularization is addressed.

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