A decomposition method for positive semidefinite matrices and its application to recursive parameter estimation

SIAM Journal on Matrix Analysis and Applications

Volumn 22, Issue 4, 2001, Pages 1095-1111

  Cao, Liyu ^a   Schwartz, Howard M ^a  

^a CARLETON UNIVERSITY   (Canada)

Author keywords

Least squares method; Matrix decomposition; Positive semidefinite matrices; Rank additivity; Recursive estimation

Indexed keywords

EID: 0035537403     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479899364027     Document Type: Article

References (10)

1. L. CAO AND H. SCHWARTZ, A directional forgetting algorithm based on the decomposition of the information matrix, Automatica J. IFAC, 36 (2000), pp. 1725-1731.
2. M. T. CHU, R. E FUNDERLIC, AND G. H. GOLUB, Rank modifications of semidefinite matrices associated with a secant update formula, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 428-436.
3. R. E. CLINE AND R. E. FUNDERLIC, The rank of a difference matrices and associated generalized inverses, Linear Algebra Appl., 24 (1979), pp. 185-215.
4. V. V. PRASOLOV, Problems and Theorems in Linear Algebra, AMS, Providence, RI, 1994.
5. R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
6. L. LJUNG AND T. SÖDERSTRÖM, Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1983.
7. K. J. ÅSTRÖM AND B. WITTENMARK, Adaptive Control, 2nd ed., Addison-Wesley, Reading, MA, 1995.
8. E. W. BAI AND S. S. SASTRY, Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control, Systems Control Lett., 6 (1985), pp. 153-163.
9. J. E. PARKUM, N. K. POULSEN, AND J. HOLST, Recursive forgetting algorithms, Internat. J. Control, 55 (1992), pp. 109-128.
10. R. M. JOHNSTONE, C. R. JOHNSON, JR., R. R. BITMEAD, AND B. D. O. ANDERSON, Exponential convergence of recursive least squares with exponential forgetting factor, Systems Control Lett., 2 (1982), pp. 77-82.