Geodesic
Majorization bounds for Ritz values of Hermitian matrices
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 1-11
Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From our results we conclude that the majorization approach appears to be advantageous, and that there is probably much more work to be carried out in this direction.
Classification : 15A18, 15A42, 15A57
Keywords: Hermitian matrices, angles between subspaces, majorization, lidskii's eigenvalue theorem, perturbation bounds, ritz values, Rayleigh-ritz method, invariant subspace 
@article{ETNA_2008__31__a23,
     author = {Paige,  Christopher C. and Panayotov,  Ivo},
     title = {Majorization bounds for {Ritz} values of {Hermitian} matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--11},
     year = {2008},
     volume = {31},
     zbl = {1171.15019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a23/}
}
TY  - JOUR
AU  - Paige,  Christopher C.
AU  - Panayotov,  Ivo
TI  - Majorization bounds for Ritz values of Hermitian matrices
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 1
EP  - 11
VL  - 31
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__31__a23/
LA  - en
ID  - ETNA_2008__31__a23
ER  - 
%0 Journal Article
%A Paige,  Christopher C.
%A Panayotov,  Ivo
%T Majorization bounds for Ritz values of Hermitian matrices
%J Electronic transactions on numerical analysis
%D 2008
%P 1-11
%V 31
%U http://geodesic.mathdoc.fr/item/ETNA_2008__31__a23/
%G en
%F ETNA_2008__31__a23
Paige,  Christopher C.; Panayotov,  Ivo. Majorization bounds for Ritz values of Hermitian matrices. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 1-11. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a23/