Geodesic
Singular value decomposition normally estimated Geršgorin sets
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 320-329.

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

Summary: Let denote a finite-dimensional square complex matrix, and let denote $$#############$\ddot ${\S}$\copyright \copyright $ a fixed singular value decomposition (SVD) of . In this note, we follow up work from Smithies and Varga $$###$$ [Linear Algebra Appl., 417 (2006), pp. 370-380], by defining the SV-normal estimator , (which satisfies !#"\%$'\)( 021 165 ), and showing how it defines an upper bound on the norm, , of the commutant ( !3"4$'\ 78$$########$$@9A$$####{B####$$ 78C of and its adjoint, . We also introduce the SV-normally estimated Ger$\check $sgorin set, , of $$#############$$HG IQPSR#TVUWX DFE `Y , defined by this SVD. Like the Ger$\check $sgorin set for , the set is a union of closed discs which $$########$$ IQPSR#TVUWa b `Y contains the eigenvalues of . When is zero, is exactly the set of eigenvalues of ; when $$###$$ ! ( IcPSR#TVUWd $$###$ "\%\ `Y is small, the set provides a good estimate of the spectrum of . We end this note by PSR8T !3"\%$)( I Uef $$###$$ Y expanding on an example from Smithies and Varga [Linear Algebra Appl., 417 (2006), pp. 370-380], and giving some examples which were generated using Matlab of the sets and , the reduced PSR8T PSR#T I Uef Icg UWXh Y Y SV-normally estimated Ger$\check $sgorin set.
Classification : 15A18, 47A07
Keywords: ger$\check $sgorin type sets, normal matrices, eigenvalue estimates 
@article{ETNA_2007__26__a7,
     author = {Fontes, Natacha and Kover, Janice and Smithies, Laura and Varga, Richard S.},
     title = {Singular value decomposition normally estimated {Ger\v{s}gorin} sets},
     journal = {Electronic transactions on numerical analysis},
     pages = {320--329},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a7/}
}
TY  - JOUR
AU  - Fontes, Natacha
AU  - Kover, Janice
AU  - Smithies, Laura
AU  - Varga, Richard S.
TI  - Singular value decomposition normally estimated Geršgorin sets
JO  - Electronic transactions on numerical analysis
PY  - 2007
SP  - 320
EP  - 329
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__26__a7/
LA  - en
ID  - ETNA_2007__26__a7
ER  - 
%0 Journal Article
%A Fontes, Natacha
%A Kover, Janice
%A Smithies, Laura
%A Varga, Richard S.
%T Singular value decomposition normally estimated Geršgorin sets
%J Electronic transactions on numerical analysis
%D 2007
%P 320-329
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2007__26__a7/
%G en
%F ETNA_2007__26__a7
Fontes, Natacha; Kover, Janice; Smithies, Laura; Varga, Richard S. Singular value decomposition normally estimated Geršgorin sets. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 320-329. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a7/