Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition

Na Li; Stefan Kindermann; Carmeliza Navasca

doi:10.1016/j.laa.2011.12.002

Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition

Na Li
, Stefan Kindermann
, Carmeliza Navasca

Institut für Industriemathematik

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

Abstract

We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.

Originalsprache	Englisch
Seiten (von - bis)	796-812
Seitenumfang	17
Fachzeitschrift	Linear Algebra and its Applications
Volume	438
Ausgabenummer	2
DOIs	https://doi.org/10.1016/j.laa.2011.12.002
Publikationsstatus	Veröffentlicht - 15 Jän. 2013

Wissenschaftszweige

101 Mathematik
102 Informatik
101014 Numerische Mathematik
101020 Technische Mathematik
102005 Computer Aided Design (CAD)

JKU-Schwerpunkte

TNF Allgemein

Zugriff auf Dokument

10.1016/j.laa.2011.12.002

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

Dieses zitieren

@article{346daa0efa4b4d139f7de92809dde5b0,

title = "Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition",

abstract = "We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.",

author = "Na Li and Stefan Kindermann and Carmeliza Navasca",

year = "2013",

month = jan,

day = "15",

doi = "10.1016/j.laa.2011.12.002",

language = "English",

volume = "438",

pages = "796--812",

journal = "Linear Algebra and its Applications",

issn = "0024-3795",

number = "2",

}

TY - JOUR

T1 - Some Convergence results on the regularized Alternating Least Squares method for tensor decomposition

AU - Li, Na

AU - Kindermann, Stefan

AU - Navasca, Carmeliza

PY - 2013/1/15

Y1 - 2013/1/15

N2 - We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.

AB - We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual Alternating Least-Squares method.

UR - https://www.scopus.com/pages/publications/84869465301

U2 - 10.1016/j.laa.2011.12.002

DO - 10.1016/j.laa.2011.12.002

M3 - Article

SN - 0024-3795

VL - 438

SP - 796

EP - 812

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 2

ER -