To solving spectral problems for $q$-parameter polynomial matrices. 2

The paper continues the studies of the method of hereditary pencils for computing points of the finite spectrum of a multiparameter polynomial matrix. The method involves induction on the number of parameters and consists of two stages. At the first stage, given the coefficients of a multiparameter matrix, a sequence of $(q-k)$-parameter polynomial matrices ($k=1,\dots,q$) satisfying certain recursive relations is formed. This sequence is used at the second stage. As the base case, two-parameter matrices and their spectral characteristics, which are computed by applying the method of hereditary pencils, are considered. Algorithms implementing the second stage are suggested and theoretically justified.