A Fast Adaptive Algorithm for the Generalized Symmetric Eigenvalue Problem

In this letter, we propose a new adaptive algorithm for the generalized symmetric eigenvalue problem, which can extract the principal and minor generalized eigenvectors, as well as their corresponding subspaces, at a low computational cost. A comparison with other adaptive algorithms from the literature, including the batch generalized singular value decomposition (GSVD) technique, is also given to show the superiority of the proposed algorithm in terms of convergence performance and computational complexity.

[1]  Tapan K. Sarkar,et al.  Adaptive spectral estimation by the conjugate gradient method , 1986, IEEE Trans. Acoust. Speech Signal Process..

[2]  Gene H. Golub,et al.  Matrix computations , 1983 .

[3]  Angelika Bunse-Gerstner,et al.  An algorithm for the symmetric generalized eigenvalue problem , 1984 .

[4]  Karim Abed-Meraim,et al.  Fast Adaptive Blind MMSE Equalizer for Multichannel FIR Systems , 2006, EURASIP J. Adv. Signal Process..

[5]  Juha Karhunen,et al.  Principal component neural networks — Theory and applications , 1998, Pattern Analysis and Applications.

[6]  Jian Yang,et al.  RLS-based adaptive algorithms for generalized eigen-decomposition , 2006, IEEE Transactions on Signal Processing.

[7]  Wang Shougen,et al.  An algorithm for Ax = lBx with symmetric and positive-definite A and B , 1991 .

[8]  Lei Xu,et al.  Least mean square error reconstruction principle for self-organizing neural-nets , 1993, Neural Networks.

[9]  Dennis R. Morgan,et al.  Downlink adaptive array algorithms for cellular mobile communications , 2003, IEEE Trans. Commun..

[10]  George Mathew,et al.  A quasi-Newton adaptive algorithm for generalized symmetric eigenvalue problem , 1996, IEEE Trans. Signal Process..

[11]  Carlos E. Davila,et al.  Efficient, high performance, subspace tracking for time-domain data , 2000, IEEE Trans. Signal Process..

[12]  Peter Strobach.  Fast orthogonal iteration adaptive algorithms for the generalized symmetric eigenproblem , 1998, IEEE Trans. Signal Process..

[13]  Michael D. Zoltowski,et al.  A Linear Receiver for Direct-Sequence Spread-Spectrum Multiple-Access Systems with Antenna Arrays and Blind Adaptation , 1998, IEEE Trans. Inf. Theory.