To solving spectral problems for $q$-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, $q\ge2$, 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. Bibl. 2 titles.