Geodesic
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 
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/
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     author = {V. N. Kublanovskaya},
     title = {To solving multiparameter problems of algebra. {2.~The} method of partial relative factorization and its applications},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

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

[2] V. N. Kublanovskaya, “K resheniyu mnogoparametricheskikh zadach algebry. 1. Metody vychisleniya nasledstvennykh polinomov i ikh primeneniya”, Zap. nauchn. semin. POMI, 284, 2002, 143–162 | Zbl

[3] V. N. Kublanovskaya, “Metody i algority resheniya spektralnykh zadach dlya polinomialnykh i ratsionalnykh matrits”, Zap. nauchn. semin. POMI, 238, 1997, 7–329

[4] V. B. Khazanov, “O sobstvennykh porozhdayuschikh vektorakh mnogoparametricheskoi matritsy”, Zap. nauchn. semin. POMI, 245, 1998, 165–186 | MR