On certain factorizations of two-parameter polynomial matrices

V. N. Kublanovskaya

Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part X, Tome 219 (1994), pp. 94-116

Résumé

The paper is an extension of the results of paper [1]. Various rank factorization algorithms of a singular two-parameter polynomial matrix into a product of matrices having the same rank coinciding with the rank of an original matrix and their spectral properties are suggested. In particular, the notion of minimal factorization is extended to one parameter polynomial and constant matrices. It allows as to isolate the regular part of the spectrum of a matrix, which contains the finite continuous spectrum of the original matrix, and the computation of its discrete spectrum is reduced to computing one of two matrices full column and row rank not containing the continuous spectrum. Bibliography: 13 titles.