Geodesic
On rank-one corrections of complex symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 78-83 
M. Dana; Kh. D. Ikramov. On rank-one corrections of complex symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 78-83. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a5/
@article{ZNSL_2006_334_a5,
     author = {M. Dana and Kh. D. Ikramov},
     title = {On rank-one corrections of complex symmetric matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {78--83},
     year = {2006},
     volume = {334},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a5/}
}
TY  - JOUR
AU  - M. Dana
AU  - Kh. D. Ikramov
TI  - On rank-one corrections of complex symmetric matrices
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 78
EP  - 83
VL  - 334
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a5/
LA  - ru
ID  - ZNSL_2006_334_a5
ER  - 
%0 Journal Article
%A M. Dana
%A Kh. D. Ikramov
%T On rank-one corrections of complex symmetric matrices
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 78-83
%V 334
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a5/
%G ru
%F ZNSL_2006_334_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let a matrix $A\in M_n(\mathbf C)$ be a rank-one perturbation of a complex symmetric matrix, i.e. $A=X+Y$ for some unknown matrices $X$ and $Y$ such that $X=X^T$ and $\mathrm{rank}\,Y=1$. The problem of determining the matrices $X$ and $Y$ is solved.

[1] M. Dana, Kh. D. Ikramov, “O malorangovykh korrektsiyakh ermitovykh i unitarnykh matrits”, Zh. vychisl. matem. matem. fiz., 44 (2004), 1331–1345 | MR | Zbl

[2] T. Barth, T. Manteuffel, “Multiple recursion conjugate gradient algorithms. I: Sufficient conditions”, SIAM J. Matrix Analys. Appl., 21 (2000), 768–796 | DOI | MR | Zbl

[3] A. Bunse-Gerstner, R. Stover, “On a conjugate gradient-type method for solving complex symmetric linear systems”, Linear Algebra Appl., 287 (1999), 105–123 | DOI | MR | Zbl

[4] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1990 | MR