Geodesic
On the location of the Ritz values in the Arnoldi process
Electronic transactions on numerical analysis, Tome 43 (2015).

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

Summary: In this paper we give a necessary and sufficient condition for a set of complex values $\theta_1,\dots,\theta_k$ to be the Arnoldi Ritz values at iteration $k$ for a general diagonalizable matrix $A$. Then we consider normal matrices and, in particular, real normal matrices with a real starting vector. We study in detail the case $k=2,$ for which we characterize the boundary of the region in the complex plane where pairs of complex conjugate Ritz values are located. Several examples with computations of the boundary of the feasible region are given. Finally we formulate some conjectures and open problems for the location of the Arnoldi Ritz values in the case $k>2$ for real normal matrices.
Classification : 65F15, 65F18, 15A18
Keywords: arnoldi algorithm, eigenvalues, Ritz values, normal matrices 
@article{ETNA_2015__43__a1,
     author = {Meurant, G\'erard},
     title = {On the location of the {Ritz} values in the {Arnoldi} process},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {43},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__43__a1/}
}
TY  - JOUR
AU  - Meurant, Gérard
TI  - On the location of the Ritz values in the Arnoldi process
JO  - Electronic transactions on numerical analysis
PY  - 2015
VL  - 43
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__43__a1/
LA  - en
ID  - ETNA_2015__43__a1
ER  - 
%0 Journal Article
%A Meurant, Gérard
%T On the location of the Ritz values in the Arnoldi process
%J Electronic transactions on numerical analysis
%D 2015
%V 43
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2015__43__a1/
%G en
%F ETNA_2015__43__a1
Meurant, Gérard. On the location of the Ritz values in the Arnoldi process. Electronic transactions on numerical analysis, Tome 43 (2015). http://geodesic.mathdoc.fr/item/ETNA_2015__43__a1/