Unifying unitary and hyperbolic transformations

Linear Algebra and Its Applications

Volumn 316, Issue 1-3, 2000, Pages 183-197

  Bojanczyk, Adam ^a   Qiao, Sanzheng ^b   Steinhardt, Allan O ^c  

^a Cornell University   (United States)

^b MCMASTER UNIVERSITY   (Canada)

^c DEFENSE ADVANCED RESEARCH PROJECTS AGENCY   (United States)

Author keywords

Cholesky factor modification; Error analysis; Hyperbolic Householder transformation; Hyperbolic rotation

Indexed keywords

EID: 0034377056     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00108-7     Document Type: Article

References (14)

1. A.W. Bojanczyk, A. Steinhardt, Hyperbolic transformations in signal processing and control, in: Transactions of the Ninth Army Conference on Applied Mathematics and Control, 1992, pp. 479-487.
2. Bojanczyk A., Brent R.P., Van Dooren P., de Hoog F. A note on downdating the Cholesky factorization. SIAM J. Sci. Statist. Comput. 8:1987;210-221.
3. Bojanczyk A., Steinhardt A.O. Stability analysis of a Householder-based algorithm for downdating the Cholesky factorization. SIAM J. Sci. Statist. Comput. 12:1991;1255-1265.
4. Chambers J.M. Regression updating. J. Amer. Statist. Assoc. 66:1971;744-748.
5. Cybenko G., Berry M. Hyperbolic Householder algorithms for factoring structured matrices. SIAM J. Matrix Anal. Appl. 11(4):1990;499-520.
6. Dongarra J.J., Bunch J.R., Moler C.B., Stewart G.W. LINPACK User's Guide. 1979;SIAM, Philadelphia, PA.
7. I. Gohberg, P. Lancaster, L. Rodman, Matrices and Indefinite Scalar Products, Birkhauser, Basel, 1984.
8. Golub G.H., Van Loan C.F. Matrix Comput. third ed. 1996;The Johns Hopkins University Press, Baltimore, Maryland.
9. Rader C.M., Steinhardt A.O. Hyperbolic Householder transformations. IEEE Trans. Acoust. Speech Signal Processing. 34:1986;1589-1602.
10. Rader C.M., Steinhardt A.O. Hyperbolic Householder transformations. SIAM J. Matrix Anal. Appl. 9:1988;269-290.
11. A. Steinhardt, Householder transformations in signal processing, IEEE ASSP Magazine, July, 1988.
12. Stewart G.W. The effects of rounding error on an algorithm for downdating a Cholesky factorization. J. Inst. Maths. Appl. 23:1979;203-213.
13. Stewart G.W. On the stability of sequential updates and downdates. IEEE Trans. Signal Processing. 43(11):1995;2642-2648.
14. Stewart M., Stewart G.W. On hyperbolic triangularization: stability and pivoting. SIAM J. Matrix Anal. Appl. 19(4):1998;847-860.