Geodesic
Geršgorin-type eigenvalue inclusion theorems and their sharpness
Electronic transactions on numerical analysis, Tome 12 (2001), pp. 113-133.

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

Summary: Here, we investigate the relationships between $G(A)$, the union of Ger$\check $sgorin disks, $K(A)$, the union of Brauer ovals of Cassini, and $B(A)$, the union of Brualdi lemniscate sets, for eigenvalue inclusions of an n $\times n$ complex matrix A. If $\sigma (A)$ denotes the spectrum of A, we show here that $\sigma (A) \subseteq B(A) \subseteq K(A) \subseteq G(A)$ is valid for any weakly irreducible n $\times n$ complex matrix A with n $\geq 2$. Further, it is evident that $B(A)$ can contain the spectra of related n $\times n$ matrices. We show here that the spectra of these related matrices can fill out $B(A)$.
Classification : 15A18
Keywords: ger$\check $sgorin disks, Brauer ovals of Cassini, brualdi lemniscate sets, minimal ger$\check $sgorin sets 
@article{ETNA_2001__12__a6,
     author = {Varga, Richard S.},
     title = {Ger\v{s}gorin-type eigenvalue inclusion theorems and their sharpness},
     journal = {Electronic transactions on numerical analysis},
     pages = {113--133},
     publisher = {mathdoc},
     volume = {12},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2001__12__a6/}
}
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Varga, Richard S. Geršgorin-type eigenvalue inclusion theorems and their sharpness. Electronic transactions on numerical analysis, Tome 12 (2001), pp. 113-133. http://geodesic.mathdoc.fr/item/ETNA_2001__12__a6/