Title: On the best rank-1 and rank-$(R 1, R 2, ..., R N)$ Approximation and applications of higher-order tensors Authors: De Lathauwer, Lieven ×De Moor, BartVandewalle, Joos # Issue Date: 2000 Publisher: Siam publications Series Title: SIAM journal on matrix analysis and applications vol:21 issue:4 pages:1324-1342 Abstract: In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely the approximation of a given higher-order tensor, in an optimal least-squares sense, by a tensor that has prespecified column rank value, row rank value, etc. For matrices, the solution is conceptually obtained by truncation of the singular value decomposition (SVD); however, this approach does not have a straightforward multilinear counterpart. We discuss higher-order generalizations of the power method and the orthogonal iteration method. Description: \emph{SIAM J. Matrix Anal. Appl.}, vol. 21, no. 4, Apr. 2000 URI: http://gateway.newisiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=CCC&SrcApp=PRODUCT_NAME&SrcURL=WOS_RETURN_URL&CKEY=DELA1324000021SL&DestLinkType=FullRecord&DestApp=CCC&SrcDesc=RETURN_ALT_TEXT&SrcAppSID=APP_SID ISSN: 0895-4798 Publication status: published KU Leuven publication type: IT Appears in Collections: ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data AnalyticsFaculty of Science, Campus Kulak Kortrijk