Geodesic
Computation of a minimal basis of the right null space of a singular multiparameter polynomial matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 272-287 
V. B. Khazanov. Computation of a minimal basis of the right null space of a singular multiparameter polynomial matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 272-287. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a18/
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     author = {V. B. Khazanov},
     title = {Computation of a minimal basis of the right null space of a singular multiparameter polynomial matrix},
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     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a18/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A modification of an algorithm, based on the resultant approach, for computing a minimal basis of the right null space of a singular multiparameter polynomial matrix is suggested. The modification suggested is based on simultaneous computation of bases of the image and kernel of a constant matrix and allows one to reduce computational costs. This modification also permits one to compute a basis of the image of a polynomial matrix. The implementation of the algorithm is illustrated on an example.

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

[2] V. B. Khazanov, “Balansovoe sootnoshenie spektralnykh kharakteristik mnogoparametricheskoi polinomialnoi matritsy”, Zap. nauchn. semin. POMI, 367, 2009, 187–194

[3] V. B. Khazanov, “Vychislenie kharakteristik regulyarnogo konechnogo spektra singulyarnoi mnogoparametricheskoi polinomialnoi matritsy”, Zap. nauchn. semin. POMI, 482, 2019, 259–271

[4] V. A. Churkin, Zhordanova klassifikatsiya konechnomernykh lineinykh operatorov: Metodicheskie ukazaniya k novomu metodu postroeniya zhordanovoi bazy dlya lineinogo operatora, Izd-vo NGU, Novosibirsk, 1991