Geodesic
The structured distance to normality of an irreducible real tridiagonal matrix
Electronic transactions on numerical analysis, Tome 28 (2008)
The problem of computing the distance in the Frobenius norm of a given real irreducible tridiagonal matrix T to the algebraic variety of real normal irreducible tridiagonal matrices is solved. Simple formulas for computing the distance and a normal tridiagonal matrix at this distance are presented. The special case of tridiagonal Toeplitz matrices also is considered.
Classification : 65F30, 65F50, 15A57, 65F35
Keywords: matrix nearness problem, distance to normality, real tridiagonal matrix, eigenvalue conditioning, Toeplitz matrix 
@article{ETNA_2008__28__a9,
     author = {Noschese,  S. and Pasquini,  L. and Reichel,  L.},
     title = {The structured distance to normality of an irreducible real tridiagonal matrix},
     journal = {Electronic transactions on numerical analysis},
     year = {2008},
     volume = {28},
     zbl = {1171.65037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__28__a9/}
}
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%A Pasquini,  L.
%A Reichel,  L.
%T The structured distance to normality of an irreducible real tridiagonal matrix
%J Electronic transactions on numerical analysis
%D 2008
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%F ETNA_2008__28__a9
Noschese,  S.; Pasquini,  L.; Reichel,  L. The structured distance to normality of an irreducible real tridiagonal matrix. Electronic transactions on numerical analysis, Tome 28 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__28__a9/