Kublanovskaya, V. N. Solution of spectral problems for polynomial matrices. (English. Russian original) Zbl 1073.65524 J. Math. Sci., New York 127, No. 3, 2024-2032 (2005); translation from Zap. Nauchn. Semin. POMI 296, 122-138 (2003). Summary: For polynomial matrices of full rank, including matrices of the form \(A- \lambda I\) and \(A- \lambda B\), numerical methods for solving the following problems are suggested: find the divisors of a polynomial matrix whose spectra coincide with the zeros of known divisors of its characteristic polynomial; compute the greatest common divisor of a sequence of polynomial matrices; solve the inverse eigenvalue problem for a polynomial matrix. The methods proposed are based on the \(\Delta W\) and \(\Delta V\) factorizations of polynomial matrices. Applications of these methods to the solution of certain algebraic problems are considered. MSC: 65F18 Numerical solutions to inverse eigenvalue problems 65F30 Other matrix algorithms (MSC2010) 15A54 Matrices over function rings in one or more variables 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra Keywords:polynomial matrices; greatest common divisor; inverse eigenvalue problem; factorizations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. N. Kublanovskaya, ”Rank division algorithms and their applications,” J. Numer. Algebra Appl., 2, 198–213 (1992). [2] V. N. Kublanovskaya, ”Methods and algorithms for solving spectral problems for polynomial and rational matrices,” Zap. Nauchn. Semin. POMI, 238, 3–329 (1997). · Zbl 0928.65064 [3] F. R. Gantmakher, The Theory of Matrices [in Russian], Nauka, Moscow (1988). · Zbl 0666.15002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.