| Title:
|
Decomposition of an updated correlation matrix via hyperbolic transformations (English) |
| Author:
|
Janovská, Drahoslava |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
101-113 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
eigensystem of a correlation matrix |
| Keyword:
|
hyperbolic transformations |
| Keyword:
|
hyperbolic Householder transformation |
| Keyword:
|
hyperbolic Givens transformation |
| Keyword:
|
hyperbolic singular value decomposition |
| MSC:
|
65F25 |
| MSC:
|
65F30 |
| idZBL:
|
Zbl 1090.65046 |
| idMR:
|
MR1894663 |
| DOI:
|
10.1023/A:1021729017319 |
| . |
| Date available:
|
2009-09-22T18:09:05Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134488 |
| . |
| Reference:
|
[1] A. W. Bojanczyk, R. Onn and A. O. Steinhardt: Existence of the hyperbolic singular value decomposition.Linear Algebra Appl. 185 (1993), 21–30. MR 1213168 |
| Reference:
|
[2] J. M. Chambers: Regression updating.J. Amer. Statist. Assoc. 66 (1971), 744–748. 10.1080/01621459.1971.10482338 |
| Reference:
|
[3] G. H. Golub, C. F. Van Loan: Matrix Computations.The Johns Hopkins University Press, Baltimore and London, 1996, 3rd edition. MR 1417720 |
| Reference:
|
[4] S. Haykin: Adaptive Filter Theory.Prentice-Hall, Englewood Cliffs, 1996. |
| Reference:
|
[5] D. Janovská, G. Opfer: A note on hyperbolic transformations.Numer. Linear Algebra Appl. 8 (2001), 127–146. MR 1812029, 10.1002/1099-1506(200103)8:2<127::AID-NLA227>3.0.CO;2-# |
| Reference:
|
[6] D. Janovská: Algorithms of hyperbolic transformations.In: Proceedings of PANM 10, Lázně Libverda 2000, Math. Inst. Acad. Sci., Prague, 2000, pp. 54–66. (Czech) |
| Reference:
|
[7] B. C. Levy: A note on the hyperbolic singular value decomposition.Linear Algebra Appl. 277 (1998), 135–142. Zbl 0933.15016, MR 1624524 |
| Reference:
|
[8] R. Onn, A. O. Steinhardt and A. W. Bojanczyk: The hyperbolic singular value decomposition and applications.IEEE Trans. Signal Processing 39 (1991), 1575–1588. 10.1109/78.134396 |
| Reference:
|
[9] J. H. Wilkinson, C. Reinsch: Handbook for Automatic Computation, Linear Algebra.Springer, New York, 1971. MR 0461856 |
| . |
