Abstract
An algorithm for hyperbolic singular value decomposition of a given complex matrix based on hyperbolic Householder and Givens transformation matrices is described in detail. The main application of this algorithm is the decomposition of an updated correlation matrix.
Similar content being viewed by others
References
A. W. Bojanczyk, R. Onn and A. O. Steinhardt: Existence of the hyperbolic singular value decomposition. Linear Algebra Appl. 185 (1993), 21–30.
J. M. Chambers: Regression updating. J. Amer. Statist. Assoc. 66 (1971), 744–748.
G. H. Golub, C. F. Van Loan: Matrix Computations. The Johns Hopkins University Press, Baltimore and London, 1996, 3rd edition.
S. Haykin: Adaptive Filter Theory. Prentice-Hall, Englewood Cliffs, 1996.
D. Janovská, G. Opfer: A note on hyperbolic transformations. Numer. Linear Algebra Appl. 8 (2001), 127–146.
D. Janovská: Algorithms of hyperbolic transformations. In: Proceedings of PANM 10, Lázn? Libverda 2000. Math. Inst. Acad. Sci., Prague, 2000, pp. 54–66. (In Czech.)
B. C. Levy: A note on the hyperbolic singular value decomposition. Linear Algebra Appl. 277 (1998), 135–142.
R. Onn, A. O. Steinhardt and A. W. Bojanczyk: The hyperbolic singular value decomposition and applications. IEEE Trans. Signal Processing 39 (1991), 1575–1588.
J. H. Wilkinson, C. Reinsch: Handbook for Automatic Computation, Linear Algebra. Springer, New York, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Janovska, D. Decomposition of an Updated Correlation Matrix via Hyperbolic Transformations. Applications of Mathematics 47, 101–113 (2002). https://doi.org/10.1023/A:1021729017319
Issue Date:
DOI: https://doi.org/10.1023/A:1021729017319