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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Solution of the problem of optimal diagonal scaling for quasireal {Hermitian} positive-definite},
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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/

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