Abstract
The inversion of polynomial and rational matrices is considered. For regular matrices, three algorithms for computing the inverse matrix in a factored form are proposed. For singular matrices, algorithms of constructing pseudoinverse matrices are considered. The algorithms of inversion of rational matrices are based on the minimal factorization which reduces the problem to the inversion of polynomial matrices. A class of special polynomial matrices is regarded whose inverse matrices are also polynomial matrices. Inversion algorithms are applied to the solution of systems with polynomial and rational matrices. Bibliography: 3 titles.
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Literature Cited
V. N. Kublanovskaya and V. B. Khazanov, “Spectral problems for pencils of matrices. V,” Preprint LOMI P-4-86 (1991);Sov. J. Numer. Anal. Math. Modelling,4, 19–52 (1989).
D. K. Faddeev and V. N. Faddeeva,Computational Methods in Linear Algebra [in Russian], Fizmatgiz, Moscow (1963).
V. N. Kublanovskaya and V. A. Belyi, “Spectral problems for rational matrices. Methods and algorithms.IV,” Preprint LOMI P-7-90 (1990);Sov. J. Numer. Anal. Math. Modelling,6, 189–207 (1991).
Additional information
Translated by V. N. Kublanovskaya.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 97–109.
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Kon'kova, T.Y., Kublanovskaya, V.N. Inversion of polynomial and rational matrices. J Math Sci 79, 1093–1100 (1996). https://doi.org/10.1007/BF02366129
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DOI: https://doi.org/10.1007/BF02366129