Geodesic
Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 259-271 
V. B. Khazanov. Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 259-271. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a17/
@article{ZNSL_2019_482_a17,
     author = {V. B. Khazanov},
     title = {Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {259--271},
     year = {2019},
     volume = {482},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a17/}
}
TY  - JOUR
AU  - V. B. Khazanov
TI  - Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2019
SP  - 259
EP  - 271
VL  - 482
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a17/
LA  - ru
ID  - ZNSL_2019_482_a17
ER  - 
%0 Journal Article
%A V. B. Khazanov
%T Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix
%J Zapiski Nauchnykh Seminarov POMI
%D 2019
%P 259-271
%V 482
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a17/
%G ru
%F ZNSL_2019_482_a17

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A modification of a known algorithm for computing the generating eigenvectors of a multiparameter polynomial matrix of full column rank is presented. This modification permits one to compute the characteristic polynomial (or its divisors) for a singular matrix. The algorithm proposed can be extended to the general case and used for computing a minimal basis of the image of a polynomial matrix and also for computing the greatest common divisor of scalar and matrix polynomials. An illustration of implementation of the algorithm is given.

[1] V. N. Kublanovskaya, “Nekotoryi podkhod k resheniyu mnogoparametricheskikh zadach”, Zap. nauchn. semin. POMI, 229, 1995, 191–246

[2] V. B. Khazanov, “O spektralnykh svoistvakh mnogoparametricheskikh polinomialnykh matrits”, Zap. nauchn. semin. POMI, 229, 1995, 284–321

[3] V. B. Khazanov, “O nekotorykh svoistvakh polinomialnykh bazisov nad polem ratsionalnykh funktsii mnogikh peremennykh”, Zap. nauchn. semin. POMI, 284, 2002, 177–191 | Zbl

[4] V. B. Khazanov, “Metody resheniya nekotorykh parametricheskikh zadach algebry”, Zap. nauchn. semin. POMI, 323, 2005, 164–181 | Zbl

[5] V. B. Khazanov, “Rezultantnyi podkhod k vychisleniyu vektornykh kharakteristik mnogoparametricheskikh polinomialnykh matrits”, Zap. nauchn. semin. POMI, 323, 2005, 182–214 | Zbl

[6] V. B. Khazanov, “Postroenie minimalnogo bazisa pravogo nul-prostranstva singulyarnoi mnogoparametricheskoi polinomialnoi matritsy”, Zap. nauchn. semin. POMI, 482, 2019, 272–287