Geodesic
Minimal Gerschgorin sets for partitioned matrices. II: The spectral conjecture
Electronic transactions on numerical analysis, Tome 3 (1995), pp. 66-82.

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

Summary: In an earlier paper from 1970, entitled "Minimal Gerschgorin sets for partitioned matrices," a Spectral Conjecture, related to norms and spectral radii of special partitioned matrices, was stated, this conjecture being at the heart of the sharpness of the boundaries of the associated minimal Gerschgorin sets under partitioning. In this paper, this Spectral Conjecture is affirmatively settled, and is applied to the sharpness of the minimal Gerschgorin set in the special case when the block-diagonal entries are null matrices. The paper following this article then makes use of the proof of the Spectral Conjecture to obtain the general sharpness of the boundaries of the associated minimal Gerschgorin sets for partitioned matrices.
Classification : 15A18
Keywords: minimal Gerschgorin sets, partitioned matrices, monotonicity 
@article{ETNA_1995__3__a5,
     author = {Krautstengl, Alan and Varga, Richard S.},
     title = {Minimal {Gerschgorin} sets for partitioned matrices. {II:} {The} spectral conjecture},
     journal = {Electronic transactions on numerical analysis},
     pages = {66--82},
     publisher = {mathdoc},
     volume = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1995__3__a5/}
}
TY  - JOUR
AU  - Krautstengl, Alan
AU  - Varga, Richard S.
TI  - Minimal Gerschgorin sets for partitioned matrices. II: The spectral conjecture
JO  - Electronic transactions on numerical analysis
PY  - 1995
SP  - 66
EP  - 82
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_1995__3__a5/
LA  - en
ID  - ETNA_1995__3__a5
ER  - 
%0 Journal Article
%A Krautstengl, Alan
%A Varga, Richard S.
%T Minimal Gerschgorin sets for partitioned matrices. II: The spectral conjecture
%J Electronic transactions on numerical analysis
%D 1995
%P 66-82
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_1995__3__a5/
%G en
%F ETNA_1995__3__a5
Krautstengl, Alan; Varga, Richard S. Minimal Gerschgorin sets for partitioned matrices. II: The spectral conjecture. Electronic transactions on numerical analysis, Tome 3 (1995), pp. 66-82. http://geodesic.mathdoc.fr/item/ETNA_1995__3__a5/