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Volume 25 Issue 7
Jul.  2003
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Yue Bo, Jiao Licheng. An algorithm for joint diagonalization of positive definite symmmetric matrices[J]. Journal of Electronics & Information Technology, 2003, 25(7): 892-895.
Citation: Yue Bo, Jiao Licheng. An algorithm for joint diagonalization of positive definite symmmetric matrices[J]. Journal of Electronics & Information Technology, 2003, 25(7): 892-895.

An algorithm for joint diagonalization of positive definite symmmetric matrices

  • Received Date: 2002-04-22
  • Rev Recd Date: 2002-08-22
  • Publish Date: 2003-07-19
  • This paper proposes a new algorithm for joint diagonalization of positive definite symmetric matrices and shows that it can be approximated by an independent component analysis problem. The good performance of the algorithm is illustrated with an example by compared with other approaches.
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  • D.T. Pham, Joint approximate diagonalization of positive definite Hermitian matrices, SIAM J.on Matrix Anal. and Appl., 2001, 22(4), 1136-1152.[2]L. Parra, C. Spence, Separation of Non-Stationary Natural Signals, Independent Components Analysis: Principles and Practice, C. Roberts, et al. Ed., Cambridge, U. K.: Cambridge Univ.Press, 2000, 135-157.[3]P. Comon, Independent component analysis-A new concept? Signal Processing, 1994, 36(3),287-314.[4]A. Hyvarinen, Fast and robust fixed-point algorithms for independent component analysis, IEEE Trans. on Neural Networks, 1999, 10(3), 626-634.[5]B. Flury, Common principal components in k groups, J. Am. Statist. Assoc., 1984, 79(5), 892-897.[6]A. Belouchrami, K. Abed-Meraim, J. Cardoso, E. Moulines, A blind source separation technique using second-order statistics, IEEE Trans. on Signal Processing, 1997, 45(2), 434-444.[7]J. Cardoso, A. Souloumiac, Blind beamforming for non-Gaussian signals, IEE Proc-F, 1993,140(6), 362-370.[8]B. Flury, W. Gautschi, An algorithm for the simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly orthogonal form, SIAM J. of Sci. Statist. Comp.,1986, 7(1), 169-184.[9]D.T. Pham, J. Cardoso, Blind separation of instantaneous mixtures of nonstationary sources,IEEE Trans. on Signal Processing, 2001, SP-49(9), 1837-1848.
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