| Title:
|
Least squares, singular values and matrix approximations (English) |
| Author:
|
Golub, Gene Howard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
13 |
| Issue:
|
1 |
| Year:
|
1968 |
| Pages:
|
44-51 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
numerical analysis |
| MSC:
|
65-35 |
| idZBL:
|
Zbl 0179.21403 |
| idMR:
|
MR0229370 |
| DOI:
|
10.21136/AM.1968.103138 |
| . |
| Date available:
|
2008-05-20T17:41:03Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103138 |
| . |
| Reference:
|
[1] C. Eckart, G. Young: The approximation of one matrix by another of lower rank.Psychometrika, 1 (1936), pp. 211-218. 10.1007/BF02288367 |
| Reference:
|
[2] K. Fan, A. Hoffman: Some metric inequalities in the space of matrices.Proc. Anier. Math. Soc., 6 (1955), pp. 111-116. Zbl 0064.01402, MR 0067841, 10.1090/S0002-9939-1955-0067841-7 |
| Reference:
|
[3] J. Francis: The QR transformation. A unitary analogue to the LR transformation.Comput. J., 4 (1961, 1962), pp. 265-271. Zbl 0104.34304, MR 0130111, 10.1093/comjnl/4.3.265 |
| Reference:
|
[4] G. Golub, W. Kahan: Calculating the singular values and pseudoinverse of a matrix.J. SIAM Numer. Anal. Ser. B, 2 (1965), pp. 205-224. MR 0183105 |
| Reference:
|
[5] B. Green: The orthogonal approximation of an oblique structure in factor analysis.Psychometrika, 17 (1952), pp. 429-440. Zbl 0049.37601, MR 0053057, 10.1007/BF02288918 |
| Reference:
|
[6] C. Lanczos: Linear Differential Operators.Van Nostrand, London, 1961, Chap. 3. Zbl 0111.08305, MR 0129153 |
| Reference:
|
[7] L. Mirsky: Symmetric gauge functions and unitarily invariant norms.Quart. J. Math. Oxford (2), 11 (1960), pp. 50-59. Zbl 0105.01101, MR 0114821, 10.1093/qmath/11.1.50 |
| Reference:
|
[8] R. Penrose: A generalized inverse for matrices.Proc. Cambridge Philos. Soc., 51 (1955), pp. 406-413. Zbl 0065.24603, MR 0069793, 10.1017/S0305004100030401 |
| Reference:
|
[9] P. Schönemann: A generalized solution of the orthogonal procrustes problem.Psychometrika, 31 (1966), pp. 1-10. MR 0215870, 10.1007/BF02289451 |
| . |
