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.
Citation:
T. Ya. Kon'kova, V. N. Kublanovskaya, “Inversion of polynomial and rational matrices”, Computational methods and algorithms. Part IX, Zap. Nauchn. Sem. POMI, 202, Nauka, St. Petersburg, 1992, 97–109; J. Math. Sci., 79:3 (1996), 1093–1100
\Bibitem{KonKub92}
\by T.~Ya.~Kon'kova, V.~N.~Kublanovskaya
\paper Inversion of polynomial and rational matrices
\inbook Computational methods and algorithms. Part~IX
\serial Zap. Nauchn. Sem. POMI
\yr 1992
\vol 202
\pages 97--109
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1725}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1259289}
\zmath{https://zbmath.org/?q=an:0844.65032|0794.65041}
\transl
\jour J. Math. Sci.
\yr 1996
\vol 79
\issue 3
\pages 1093--1100
\crossref{https://doi.org/10.1007/BF02366129}
Linking options:
https://www.mathnet.ru/eng/znsl1725
https://www.mathnet.ru/eng/znsl/v202/p97
This publication is cited in the following 3 articles:
“To the memory of V. N. Kyblanovskaya”, J. Math. Sci. (N. Y.), 191:1 (2013), 1–3
Hunek W.P., Latawiec K.J., “A Study on New Right/Left Inverses of Nonsquare Polynomial Matrices”, International Journal of Applied Mathematics and Computer Science, 21:2 (2011), 331–348
Wojciech P. Hunek, “A New General Class of MVC-Related Inverses of Nonsquare Polynomial Matrices Based on the Smith Factorization”, IFAC Proceedings Volumes, 42:13 (2009), 372
Citation in format AMSBIB
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