Optimizing the coupling between two isometric projections of matrices

SIAM Journal on Matrix Analysis and Applications

Volumn 30, Issue 1, 2008, Pages 324-345

  Fraikin, Catherine ^a   Nesterov, Yurii ^b   Van Dooren, Paul ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b Bâtiment CORE   (Belgium)

Author keywords

Generalized numerical range; Isometry; Singular value decompostion; Trace maximization

Indexed keywords

CONTROL THEORY; EQUATIONS OF STATE; OPTIMIZATION;

COMPLEX MATRICES; CRITICAL POINTS; DIMENSIONAL SUBSPACES; FIELD OF VALUES; GENERALIZED NUMERICAL RANGE; HERMITIAN; ISOMETRY; ITERATIVE ALGORITHMS; NORMAL MATRICES; OBJECTIVE FUNCTIONS; OPTIMAL VALUES; OPTIMIZATION PROBLEMS; SIMILARITY MATRIXES; SINGULAR VALUE DECOMPOSTION; SQUARE MATRICES; TRACE MAXIMIZATION; UPPER AND LOWER BOUNDS;

SINGULAR VALUE DECOMPOSITION;

EID: 61849145142     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050643878     Document Type: Article

References (20)

1. K. ANSTREICHER AND H. WOLKOWICZ, On Lagrangian relaxation of quadratic matrix constraints, SIAM J. Matrix Anal. Appl., 22 (2000), pp. 41-55.
2. V. D. BLONDEL, A. GAJARDO, M. HEYMANS, P. SENELLART, AND P. VAN DOOREN, A measure of similarity between graph vertices: Applications to synonym extraction and Web searching, SIAM Rev., 46 (2004), pp. 647-666.
3. R. W. BROCKETT, Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems, Linear Algebra Appl., 146 (1991), pp. 79-91.
4. T. CAELLI AND S. KOSINOV, An eigenspace projection clustering method for inexact graph matching, IEEE Trans. Pattern Analysis and Machine Intelligence, 26 (2004), pp. 515-519.
5. W.-S. CHEUNG AND N. K. TSING, The C-numerical range of matrices is star-shaped, Linear Multilinear Algebra, 41 (1996), pp. 245-250.
6. D. CONTE, P. FOGGIA, C. SANSONE, AND M. VENTO, Thirty years of graph matching in pattern recognition, Int. J. Pattern Recognition and Artificial Intelligence, 18 (2004), pp. 265-298.
7. S. J. GLASER, T. SCHULTE-HERBRÜGGEN, M. SIEVEKING, O. SCHEDLETZKY, N. C. NIELSEN, O. W. SØRENSEN, AND C. GRIESINGER, Unitary control in quantum ensembles: Maximizing signal intensity in coherent spectroscopy, Science, 280 (1998), pp. 421-424.
8. M. GOLDBERG AND E. G. STRAUS, Elementary inclusion relations for generalized numerical ranges, Linear Algebra Appl., 18 (1977), pp. 1-24.
9. U. HELMKE, K. HÜPER, J. B. MOORE, AND TH. SCHULTE-HERBRÜGGEN, Gradient flows computing the C-numerical range with applications in NMR spectroscopy, J. Global Optim., 23 (2002), pp. 283-308.
10. U. HELMKE AND J. MOORE, Optimization and Dynamical Systems, Springer-Verlag, Berlin, 1994.
11. R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, New York, 1985.
12. R. A. HORN AND C. R. JOHNSON, Topics in Matrix Analysis, Cambridge University Press, New York, 1991.
13. C. K. LI, C-numerical ranges and C-numerical radii, Linear Multilinear Algebra, 37 (1994), pp. 51-82.
14. C. K. LI AND L. RODMAN, Multiplicative preservers of C-numerical ranges and radii, Linear Multilinear Algebra, 52 (2004), pp. 265-279.
15. C. K. LI AND N. K. TSING, Norms that are invariant under unitary similarities and the C-numerical radii, Linear Multilinear Algebra, 24 (1989), pp. 209-222.
16. C.-K. LI AND H. J. WOERDEMAN, A lower bound on the C-numerical radius of nilpotent matrices appearing in coherent spectroscopy, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 793-800.
17. A. MARSHALL AND I. OLKIN, Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979.
18. F. RENDL AND H. WOLKOWICZ, Applications of parametric programming and eigenvalue maximization to the quadratic assignment problem, Math. Program., 53 (1992), pp. 63-78.
19. R. WESTWICK, A theorem on numerical range, Linear Multilinear Algebra, 2 (1975), pp. 311-315.
20. Q. ZHAO, S. E. KARISCH, F. RENDL, AND H. WOLKOWICZ, Semidefinite programming relaxations for the quadratic assignment problem, J. Comb. Optim., 2 (1998), pp. 71-109.