Geodesic
Methods for solving spectral problems for multiparameter matrix pencils
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 139-168

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Method for solving the partial eigenproblem for multiparameter regular pencils of real matrices, which allow to improve given approximations of an eigenvector and the associated point of the spectrum (both finite and infinite) are suggested. The possibility of extending the methods to complex matrices, polynomial matrices, and coupled multiparameter problems is indicated. 
@article{ZNSL_2003_296_a8,
     author = {V. B. Khazanov},
     title = {Methods for solving spectral problems for multiparameter matrix pencils},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {139--168},
     publisher = {mathdoc},
     volume = {296},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a8/}
}
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V. B. Khazanov. Methods for solving spectral problems for multiparameter matrix pencils. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 139-168. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a8/