Geodesic
To solving problems of algebra for two-parameter matrices. 3
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 166-207 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper continues the series of papers devoted to surveying and developing methods for solving algebraic problems for two-parameter polynomial and rational matrices of general form. Linearization methods are considered, which allows one to reduce the problem of solving an equation $F(\lambda,\mu)x=0$, with a polynomial two-parameter matrix $F(\lambda,\mu)$, to solving an equation of the form $D(\lambda,\mu)y=0$, where $D(\lambda,\mu)=A(\mu)-\lambda B(\mu)$ is a pencil of polynomial matrices. Consistent pencils and their application to solving spectral problems for the matrix $F(\lambda,\mu)$ are discussed. The notion of reducing subspace is generalized to the case of a pencil of polynomial matrices. An algorithm for transforming a general pencil of polynomial matrices to a quasitriangular pencil is suggested. For a pencil with multiple eigenvalues, algorithms for computing the Jordan chains are developed. Bibl. – 8 titles. 
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V. N. Kublanovskaya; V. B. Khazanov. To solving problems of algebra for two-parameter matrices. 3. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 166-207. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a12/

[1] V. N. Kublanovskaya, “Metody i algoritmy resheniya spektralnykh zadach dlya polinomialnykh i ratsionalnykh matrits”, Zap. nauchn. semin. POMI, 238, POMI, SPb., 1997, 7–328 | MR | Zbl

[2] V. N. Kublanovskaya, V. B. Khazanov, Spektralnye zadachi dlya puchkov matrits. Metody i algoritmy, Preprint LOMI R-2-88, 1988

[3] V. N. Kublanovskaya, V. B. Khazanov, “Spektralnye zadachi dlya puchkov polinomialnykh matrits. Metody i algoritmy. V”, Zapiski nauchn. semin. LOMI, 202, Nauka, L., 1992, 26–70 | MR | Zbl

[4] V. N. Kublanovskaya, V. B. Khazanov, Chislennye metody resheniya parametricheskikh zadach algebry. Chast 1. Odnoparametricheskie zadachi, Nauka, SPb., 2004

[5] V. N. Simonova, Modifikatsii $AB$-algoritma i ikh primenenie k resheniyu sistem nelineinykh algebraicheskikh uravnenii, Avtoreferat kandidatskoi dissertatsii, L., 1990

[6] C. Moler, G. Stewart, “An algorithm for the generalized matrix eigenvalue problem”, SIAM J. Numer. Anal., 10 (1973), 241–256 | DOI | MR | Zbl

[7] G. Stewart, “On the sensitivity of the eigenvalue problem $Ax=\lambda Bx$”, SIAM J. Numer. Anal., 9 (1972), 669–686 | DOI | MR | Zbl

[8] P. Van Dooren, “Reducing subspaces: definitions, properties, and algorithms”, Lect. Notes Math., 973, 1983, 58–73 | Zbl