A modified Newton's method for best rank-one approximation to tensors

Applied Mathematics and Computation

Volumn 216, Issue 6, 2010, Pages 1859-1867

  Chang, Jingya ^a   Sun, Wenyu ^a   Chen, Yannan ^b  

^a NANJING NORMAL UNIVERSITY   (China)

^b NANJING FORESTRY UNIVERSITY   (China)

Author keywords

Modified Newton's method; Numerical multilinear algebra; Projective direction; Rank one approximation; Tensor computation

Indexed keywords

ALTERNATING LEAST SQUARES; APPROXIMATION PROBLEMS; GAUSS-NEWTON; GLOBAL CONVERGENCE; ITERATIVE MATRICES; LINE SEARCHES; MODIFIED NEWTON'S METHOD; MULTILINEAR ALGEBRA; NEWTON ALGORITHM; NEWTON METHODS; NUMERICAL COMPARISON; NUMERICAL EXPERIMENTS; NUMERICAL MULTILINEAR ALGEBRA;

ALGEBRA; ALGORITHMS; NEWTON-RAPHSON METHOD;

TENSORS;

EID: 77953136528     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.12.019     Document Type: Article

References (17)

1. Berge J.T., Leeuw J.D., and Kroonenberg P. Some additional results and principal components analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 52 (1987) 183-191
2. Cardoso J.F., and Souloumiac A. Jacobi angles for simultaneous diagonalization. SIAM J. Matrix Anal. Appl. 17 (1996) 161-164
3. Carroll J.D., and Chang J. Analysis of individual differences in multidimensional scaling via an N-way genaralization of Eckart-Yong decomposition. Psychometrika 35 (1970) 283-319
4. Kiers H. An alternating least squares algorithm for PARAFAC2 and three-way DEDICOM. Comput. Statist. Data Anal. 16 (1993) 103-118
5. Kroonenberg P.M. Three-mode Principal Component Analysis (1983), DSWO Press, Leiden, The Netherlands
6. Kroonenberg P.M. Three-mode principal component analysis: illustrated with an example from attachment theory. In: Law H.G., Synder C.W., Hattie J.A., and McDonald R.P. (Eds). Research Methods for Multimode Data Analysis (1984), Praeger, New York 64-103
7. Kroonenberg P.M., and Leeuw J.D. Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 45 (1980) 69-97
8. Lathauwer L.D., Comon P., Moor B.D., et al. High-order power method - application in independent component analysis. Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA'95) (1995), Las Vegas, NV 91-96
9. N) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21 (2000) 1324-1342
10. Lathauwer L.D., Moor B.D., and Vandewalle J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21 (2000) 1253-1378
11. Tucker L.R. Some mathematical notes on three mode factor analysis. Psychometrika 31 (1966) 279-311
12. Qi L., Sun W., and Wang Y. Numerical multilinear algebra and its applications. Front. Math. China 2 (2007) 501-526
13. Qi L. Eigenvalues of a real supersymmetric tensor. J. Symbo. Comput. 40 (2005) 1302-1324
14. Qi L. Rank and eigenvalues of a supersymmetric tensor, a multivariate homogeneous polynomial and an algebraic surface defined by them. J. Symb. Comput. 41 (2006) 1309-1327
15. Qi L. Eigenvalues and invariants of tensors. J. Math. Anal. Appl. 325 (2007) 1363-1377
16. Sun W., and Yuan Y. Optimization Theory and Methods: Nonlinear Programming (2006), Springer
17. Zhang T., and Golub G.H. Rank-one approximation to higher order tensors. SIAM J. Matrix Anal. Appl. 23 (2001) 534-550