Geodesic
Methods and algorithms of solving spectral problems for polynomial and rational mathrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XII, Tome 238 (1997), pp. 7-328 
V. N. Kublanovskaya. Methods and algorithms of solving spectral problems for polynomial and rational mathrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XII, Tome 238 (1997), pp. 7-328. http://geodesic.mathdoc.fr/item/ZNSL_1997_238_a0/
@article{ZNSL_1997_238_a0,
     author = {V. N. Kublanovskaya},
     title = {Methods and algorithms of solving spectral problems for polynomial and rational mathrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--328},
     year = {1997},
     volume = {238},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_238_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The present paper studies some methods and algorithms for numerical solution of spectral problems and problems related to them for one- and two-parameter polynomial and rational matrices. A review of some known methods based on rank factorization of constant matrices (the SVD and QR-decomposition algorithms) is suggested. The rank factorization approach is generalized to one- and two-parameter polynomial and rational matrices. Methods and algorithms for solving some parametric problems of algebra are constructed by using rank-factorization methods.