To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 89-107
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For a $q$-parameter ($q\ge2$) polynomial matrix of full rank whose regular and singular spectra have no points in common, a method for computing its partial relative factorization into a product of two matrices with disjoint spectra is suggested. One of the factors is regular and is represented as a product of $q$ matrices with disjoint spectra. The spectrum of each of the factors is independent of one of the parameters and forms in the space $\mathbb C^q$ a cylindrical manifold w.r.t. this parameter. The method is applied to computing zeros of the minimal polynomial with the corresponding eigenvectors. An application of the method to computing a basis of the null-space of polynomial solutions of the matrix that contains no zeros of its minimal polynomial is considered.
@article{ZNSL_2003_296_a5,
author = {V. N. Kublanovskaya},
title = {To solving multiparameter problems of algebra. {2.~The} method of partial relative factorization and its applications},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {89--107},
publisher = {mathdoc},
volume = {296},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a5/}
}
TY - JOUR AU - V. N. Kublanovskaya TI - To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications JO - Zapiski Nauchnykh Seminarov POMI PY - 2003 SP - 89 EP - 107 VL - 296 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a5/ LA - ru ID - ZNSL_2003_296_a5 ER -
%0 Journal Article %A V. N. Kublanovskaya %T To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications %J Zapiski Nauchnykh Seminarov POMI %D 2003 %P 89-107 %V 296 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a5/ %G ru %F ZNSL_2003_296_a5
V. N. Kublanovskaya. To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 89-107. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a5/