Methods and algorithms of solving spectral problems for polynomial and rational mathrices

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.