Geodesic
Solution of the eigenvalue problem for the regular bundle $D(\lambda)=\lambda A_0-A_1$ using deflated subspaces
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 48-65 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider the solution of the generalized eigenvalue problem $$ (A_0\lambda-A_1)x=0, $$ in the case where one or both of the matrices $A_0$, $A_1$ are degenerate but the intersection of their null spaces is empty. Using orthogonal matrices $\mathscr P$ and which are independent of $\lambda$ the original problem is transformed to a simpler one in which the pencil is of smaller dimension. The construction of $P$ and $Q$ uses the normalization process. We include an Algol program and sample runs. 
@article{ZNSL_1978_80_a2,
     author = {T. Ya. Kon'kova},
     title = {Solution of the eigenvalue problem for the regular bundle $D(\lambda)=\lambda A_0-A_1$ using deflated subspaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {48--65},
     year = {1978},
     volume = {80},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a2/}
}
TY  - JOUR
AU  - T. Ya. Kon'kova
TI  - Solution of the eigenvalue problem for the regular bundle $D(\lambda)=\lambda A_0-A_1$ using deflated subspaces
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1978
SP  - 48
EP  - 65
VL  - 80
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a2/
LA  - ru
ID  - ZNSL_1978_80_a2
ER  - 
%0 Journal Article
%A T. Ya. Kon'kova
%T Solution of the eigenvalue problem for the regular bundle $D(\lambda)=\lambda A_0-A_1$ using deflated subspaces
%J Zapiski Nauchnykh Seminarov POMI
%D 1978
%P 48-65
%V 80
%U http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a2/
%G ru
%F ZNSL_1978_80_a2
T. Ya. Kon'kova. Solution of the eigenvalue problem for the regular bundle $D(\lambda)=\lambda A_0-A_1$ using deflated subspaces. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 48-65. http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a2/