Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations

Numerische Mathematik

Volumn 115, Issue 2, 2010, Pages 309-331

  Uschmajew, André ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952096996     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-009-0276-9     Document Type: Article

References (22)

1. Chinnamsetty S. R., Espig M., Flad H.-J., Khoromskij B. N., Hackbusch W.: Tensor product approximation with optimal rank in quantum chemistry. J. Chem. Phys. 127, 084110 (2007).
2. De Lathauwer L., De Moor B., Vandewalle J.: A multilinear singular value decomposition. SIAM. J. Matrix Anal. Appl. 21(4), 1253-1278 (2000).
3. N) approximation of high-order tensors. SIAM J. Matrix Anal. Appl. 21(4), 1324-1342 (2000).
4. De Silva, V., Lim, L.-H.: Tensor rank and the ill-posedness of the best low-rank approximation problem. SCCM-06-06, Stanford (2006).
5. Edelman A., Arias T., Smith S. T.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20, 303-353 (1999).
6. Espig, M.: Effiziente Bestapproximation mittels Summen von Elementartensoren in hohen Dimensionen. Phd. Thesis, MPI-MIS Leipzig, Germany (2007).
7. Gohberg I. C., Krein M. G.: Introduction to the Theory of Linear Nonselfadjoint Operators. American Mathematical Society, Providence (1969).
8. Golub G. H., Zhang T.: Rank-one approximation to high order tensors. SIAM J. Matrix Anal. Appl. 23, 534-550 (2001).
9. Greub W. H.: Multilinear Algebra. Springer-Verlag, Berlin (1967).
10. Hackbusch W., Khoromskij B. N.: Tensor-product approximation to operators and functions in high dimensions. J. Complexity 23, 697-714 (2007).
11. Håstad J.: Tensor rank is NP-complete. J. Algorithms 11, 644-654 (1990).
12. Horn R. A., Johnson C. R.: Matrix Analysis. Cambridge University Press, Cambridge (1990).
13. Horn R. A., Johnson C. R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1994).
14. Kolda T. G.: Orthogonal tensor decompositions. SIAM J. Matrix Anal. Appl. 23(1), 243-255 (2001).
15. Kolda T. G.: A counterexample to the possibility of an extension of the Eckart-Young low-rank approximation theorem for the orthogonal rank tensor decomposition. SIAM J. Matrix Anal. Appl. 24(3), 762-767 (2003).
16. Kolda, T. G., Bader, B. W.: Tensor decompositions and applications. SIAM Rev. 51(3) (2009).
17. Kolmogorov A. N., Fomin S. V.: Elements of the Theory of Functions and Functional Analysis. Volume 1 Metric and Normed Spaces. Graylock Press, Rochester (1957).
18. Le Bris C.: A general approach for multiconfiguration methods in quantum molecular chemistry. Ann. Inst. Henri Poincaré 11(4), 441-484 (1994).
19. Lieb E. H., Simon B.: The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys. 53, 185-194 (1977).
20. Temlyakov V. N.: Greedy algortihms and M-term approximation with regard to redundant dictionaries. J. Approx. Theory 98, 117-145 (1999).
21. Weidmann J.: Lineare Operatoren in Hilberträumen, Teil 1. Teubner Verlag, Stuttgart (2000).
22. Zeidler E.: Applied Functional Analysis. Main Principles and Their Applications. Springer-Verlag, New York (1995).