Geodesic
On the singular two-parameter eigenvalue problem
The electronic journal of linear algebra, Tome 18 (2009), pp. 420-437.

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

Summary: In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. In this paper, the above relation to singular two-parameter eigenvalue problems is extended, and it is shown that the simple finite regular eigenvalues of a two-parameter eigenvalue problem and the associated system of generalized eigenvalue problems agree. This enables one to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems.
Classification : 15A18, 15A69, 65F15
Keywords: singular two-parameter eigenvalue problem, operator determinant, Kronecker canonical form, minimal reducing subspace 
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     title = {On the singular two-parameter eigenvalue problem},
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Muhic, Andrej; Plestenjak, Bor. On the singular two-parameter eigenvalue problem. The electronic journal of linear algebra, Tome 18 (2009), pp. 420-437. http://geodesic.mathdoc.fr/item/ELA_2009__18__a24/