Geodesic
The structured distance to nearly normal matrices
Electronic transactions on numerical analysis, Tome 36 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this note we examine the algebraic variety of complex tridiagonal matrices , such that $\textcent $###$\sterling $###$${\S}$$###$\ddot $###$ \copyright $, where is a fixed real diagonal matrix. If then is , the set of tridiagonal normal $\sterling \copyright $#############$\copyright $########$ - \copyright -- \copyright $#################################!####" $\textcent \\% matrices. For , we identify the structure of the matrices in and analyze the suitability for eigenvalue \sterling ###(' ###)$" textcent$estimation using normal matrices for elements of . We also compute the Frobenius norm of elements of , $££textcenttextcent$describe the algebraic subvariety consisting of elements of with minimal Frobenius norm, and calculate the $££0 textcent$distance from a given complex tridiagonal matrix to .\par $textcent$###$$\sterling$
Classification : 65F30, 65F35, 15A57, 15A18, 47A25
Keywords: nearness to normality, tridiagonal matrix, kre$\check $ın spaces, eigenvalue estimation, ger$\check $sgorin type sets 
@article{ETNA_2010__36__a5,
     author = {Smithies, Laura},
     title = {The structured distance to nearly normal matrices},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {36},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__36__a5/}
}
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AU  - Smithies, Laura
TI  - The structured distance to nearly normal matrices
JO  - Electronic transactions on numerical analysis
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%0 Journal Article
%A Smithies, Laura
%T The structured distance to nearly normal matrices
%J Electronic transactions on numerical analysis
%D 2010
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%F ETNA_2010__36__a5
Smithies, Laura. The structured distance to nearly normal matrices. Electronic transactions on numerical analysis, Tome 36 (2010). http://geodesic.mathdoc.fr/item/ETNA_2010__36__a5/