Geodesic
Solution of the problem of optimal diagonal scaling for quasireal Hermitian positive-definite
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 84-126

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper completely solves the problem of optimal diagonal scaling for quasireal Hermitian positive-definite matrices of order 3. In particular, in the most interesting irreducible case, it is demonstrated that for any matrix $C$ from the class considered there is a uniquely determined optimally scaled matrix $D^*_0CD_0$ of one of the four canonical types, and formulas for the entries of the diagonal matrix $D_0$ are presented as well as formulas for the eigenvalues and eigenvectors of $D^*_0CD_0$ and for the optimal condition number of $C$, which is equal to $k(D^*_0CD_0)$. The optimality of the Jacobi scaling is analyzed. 
@article{ZNSL_2004_309_a5,
     author = {L. Yu. Kolotilina},
     title = {Solution of the problem of optimal diagonal scaling for quasireal {Hermitian} positive-definite},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {84--126},
     publisher = {mathdoc},
     volume = {309},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a5/}
}
TY  - JOUR
AU  - L. Yu. Kolotilina
TI  - Solution of the problem of optimal diagonal scaling for quasireal Hermitian positive-definite
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 84
EP  - 126
VL  - 309
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a5/
LA  - ru
ID  - ZNSL_2004_309_a5
ER  - 
%0 Journal Article
%A L. Yu. Kolotilina
%T Solution of the problem of optimal diagonal scaling for quasireal Hermitian positive-definite
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 84-126
%V 309
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a5/
%G ru
%F ZNSL_2004_309_a5
L. Yu. Kolotilina. Solution of the problem of optimal diagonal scaling for quasireal Hermitian positive-definite. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 84-126. http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a5/