Riccati-like flows and matrix approximations
Kybernetika, Tome 29 (1993) no. 6, pp. 563-582 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 34A30, 65F30, 93B11, 93B25, 93B40, 93C15
@article{KYB_1993_29_6_a3,
     author = {Helmke, Uwe and Prechtel, Michael and Shayman, Mark A.},
     title = {Riccati-like flows and matrix approximations},
     journal = {Kybernetika},
     pages = {563--582},
     year = {1993},
     volume = {29},
     number = {6},
     mrnumber = {1264887},
     zbl = {0802.65058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1993_29_6_a3/}
}
TY  - JOUR
AU  - Helmke, Uwe
AU  - Prechtel, Michael
AU  - Shayman, Mark A.
TI  - Riccati-like flows and matrix approximations
JO  - Kybernetika
PY  - 1993
SP  - 563
EP  - 582
VL  - 29
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_1993_29_6_a3/
LA  - en
ID  - KYB_1993_29_6_a3
ER  - 
%0 Journal Article
%A Helmke, Uwe
%A Prechtel, Michael
%A Shayman, Mark A.
%T Riccati-like flows and matrix approximations
%J Kybernetika
%D 1993
%P 563-582
%V 29
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_1993_29_6_a3/
%G en
%F KYB_1993_29_6_a3
Helmke, Uwe; Prechtel, Michael; Shayman, Mark A. Riccati-like flows and matrix approximations. Kybernetika, Tome 29 (1993) no. 6, pp. 563-582. http://geodesic.mathdoc.fr/item/KYB_1993_29_6_a3/

[1] G. Eckart, G. Young: The approximation of one matrix by another of lower rank. Psychometrika / (1936), 211-218.

[2] G. H. Golub, C. Van Loan: An analysis of the total least squares problem. SIAM J. Numer. Anal. 17 (1980), 883-843. | MR | Zbl

[3] G. H. Golub A. Hoffmann, G. W. Stewart: A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Linear Algebra Appl. 88/89 (1987), 317-327. | MR

[4] U. Helmke, J. B. Moore: Optimization and Dynamical Systems. Springer-Verlag, Berlin 1993. | MR

[5] U. Helmke, M. A. Shayman: Critical points of matrix least squares distance functions. Linear Algebra Appl., to appear. | MR | Zbl

[6] N. J. Higham: Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl. 103 (1988), 103-118. | MR | Zbl

[7] B. De Moor, J. David: Total linear least squares and the algebraic Riccati equation. Systems Control Lett. 5 (1992), 329-337. | MR | Zbl

[8] J. B. Moore R. E. Mahony, U. Helmke: Recursive gradient algorithms for eigenvalue and singular value decomposition. SIAM J. Matrix Anal. Appl., to appear. | MR