Joint eigenvalue decomposition using polar matrix factorization

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6365 LNCS, Issue , 2010, Pages 555-562

  Luciani, Xavier ^a,b   Albera, Laurent ^a,b  

^a INSERM   (France)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

Jacobi method; Joint diagonalization by similarity; joint eigenvalue decomposition; polar matrix decomposition

Indexed keywords

FACTORIZATION; JACOBIAN MATRICES;

COMPARISON RESULT; COMPARISON STUDY; EIGENVALUE DECOMPOSITION; JACOBI METHODS; JOINT DIAGONALIZATION; ORIGINAL ALGORITHMS; POLAR MATRIX; REFERENCE ALGORITHM;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 78349255583     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-15995-4_69     Document Type: Conference Paper

References (16)

1. van der Veen, A.J., Ober, P.B., Deprettere, E.F.: Azimuth and elevation computation in high resolution DOA estimation. IEEE Trans. Signal Proc. 40, 1828-1832 (1992)
2. Lemma, A.N., van der Veen, A.J., Deprettere, E.F.: Analysis of joint angle-frequency estimation using ESPRIT. IEEE Trans. Signal Proc. 51, 1264-1283 (2003)
3. Haardt, M., Nossek, J.A.: Simultaneous Schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieveal problems. IEEE Trans. Signal Proc. 46, 161-169 (1998)
4. Albera, L., Ferréol, A., Chevalier, P., Comon, P.: ICAR, a tool for blind source separation using fourth order statistics only. IEEE Trans. Signal Proc. 53(10-1), 3633-3643 (2005)
5. Roemer, F., Haardt, M.: A closed-form solution for multilinear PARAFAC decompositions. In: IEEE SAM 2008, pp. 487-491 (2008)
6. Bunse-Gerstner, A., Byers, R., Mehrmann, V.: Numerical Methods for Simultaneous Diagonalization. SIAM J. Matrix Anal. Applicat. 14 (4), 927-949
7. Yeredor, A.: Non-Orthogonal Joint Diagonalization in the Least-Squares Sense with Application in Blind Source Separation. IEEE Trans. Signal Proc. 50(7), 1545-1553 (2002)
8. Karfoul, A., Albera, L., Birot, G.: Blind underdetermined mixture identification by joint canonical decomposition of HO cumulants. IEEE Trans. Signal Proc. 58(2), 638-649 (2010)
9. Strobach, P.: Bi-iteration multiple invariance subspace tracking and adaptive ESPRIT. IEEE Trans. Signal Proc. 48, 442-456 (2000)
10. Fu, T., Gao, X.: Simultaneous Diagonalization with Similarity Transformation for Non-defective Matrices. In: IEEE ICASSP 2006, pp. 1137-1140 (2006)
11. Goldstine, H.H., Horwitz, L.P.: A procedure for the diagonalization of normal matrices. J. ACM 6(2), 176-195 (1959)
12. Eberlein, P.J.: A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix. Journal of the Society for Industrial and Applied Mathematics 10(1), 74-88 (1962)
13. Ruhe, A.: On the quadratic convergence of a generalization of the Jacobi method to arbitrary matrices. BIT Numerical Mathematics 8, 210-231 (1968)
14. Souloumiac, A.: Nonorthogonal joint Diagonalization by Combining Givens and Hyperbolic Rotations. IEEE Trans. Signal Proc. 57(6), 2222-2231 (2009)
15. Iferroudjene, R., Abed Meraim, K., Belouchrani, A.: A New Jacobi-like Method for Joint Diagonalization of Arbitrary non-defective Matrices. Applied Mathematics and Computation 211, 363-373 (2009)
16. Cardoso, J.-F., Souloumiac, A.: Jacobi Angles for Simultaneous Diagonalization. SIAM Journal on Matrix Analysis and Applications 17(1), 161-164 (1996)