To solving spectral problems for <Emphasis Type="Italic">q</Emphasis>-parameter polynomial matrices

The method of hereditary pencils, originally suggested by the author for solving spectral problems for two-parameter matrices (pencils of matrices), is extended to the case of q-parameter, q ≥ 2, polynomial matrices. Algorithms for computing points of the finite regular and singular spectra of a q-parameter polynomial matrix and their theoretical justification are presented. Bibliography: 2 titles.