Generalizations of the Rayleigh quotient iteration for the iterative refinement of the eigenvectors of real symmetric matrices

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

Volumn V, Issue , 2005, Pages

  Nikpour, Maziar ^a   Hüper, Knut ^b   Manton, Jonathan H ^c  

^a Catholic University of Louvain   (Belgium)

^b CSIRO   (Australia)

^c UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; REAL TIME SYSTEMS; SET THEORY;

CUBIC RATES; EIGENVALUE-EIGENVECTOR PAIRS; RAYLEIGH QUOTIENT ITERATION; REAL SYMMETRIC MATRICES;

ITERATIVE METHODS;

EID: 33646821746     PISSN: 15206149     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICASSP.2005.1416485     Document Type: Conference Paper

References (7)

1. M. Nikpour, J.H. Manton, and R. Mahony, "Novel Newton Algorithms for the Hermitian Eigenvalue Problem," in Proceedings of Information, Decision and Control, Adelaide, Australia, February 2002.
2. nd IEEE Conference on Decision and Control, Maui, USA, December 2003, vol. 3, pp. 2364-2367.
3. D.S. Watkins, "Understanding the QR algorithm," SIAM Review, vol. 24, no. 4, pp. 427-440, 1982.
4. K. Hüper, "A calculus approach to matrix eigenvalue algorithms," Habilitation Dissertation, July 2002, Mathematisches Institut, Universität Würzburg, Germany, http://www.rsise.anu.edu.au/~hueper/.
5. K. Hüper, Mathematical Systems Theory in Biology, Communications, Computation, vol. 134 of The IMA Volumes in Mathematics and its Applications, chapter: A Dynamical System Approach to Matrix Eigenvalue Algorithms, pp. 257-274, Springer, New York, 2003.
6. M. Nikpour, Reduced Rank Signal Processing, Ph.D. thesis, The University of Melbourne, Australia, 2002.
7. M. Shub, "Some remarks on dynamical systems and numerical analysis," in Dynamical systems and partial differential equations (Caracas, 1984), pp. 69-91. Univ. Simon Bolivar, Caracas, 1986.