A counterexample to the possibility of an extension of the Eckart-young low-rank approximation theorem for the orthogonal rank tensor decomposition

SIAM Journal on Matrix Analysis and Applications

Volumn 24, Issue 3, 2003, Pages 762-767

  Kolda, Tamara G ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Higher order tensor; Multidimensional arrays; Multilinear algebra; Principal components analysis; Singular value decomposition

Indexed keywords

EID: 0042915998     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479801394465     Document Type: Article

References (5)

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3. C. ECKART AND G. YOUNG, The approximation of one matrix by another of lower rank, Psychometrika, 1 (1936), pp. 211-218.
4. T. G. KOLDA, Orthogonal tensor decompositions, SIAM J. Matrix Analysis, 23 (2001), pp. 243-255.
5. D. LEIBOVICI AND R. SABATIER, A singular value decomposition of a k-way array for principal component analysis of multiway data, PTA-k, Linear Algebra Appl., 269 (1998), pp. 307-329.