Abstract
It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package.
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References
B. Zhou, J. Lam, and G.-R. Duan, “Toward solution of matrix equation X = Af(X)B + C,” Linear Algebra Appl. 435, 1370–1398 (2011).
Kh. D. Ikramov, Numerical Solution ofMatrix Equations (Nauka, Moscow, 1984) [in Russian].
G. H. Golub and Ch. van Loan, Matrix Computations (John Hopkins Univ. Press, Baltimor, London, 1983).
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Original Russian Text © Kh.D. Ikramov, Yu.O. Vorontsov, 2018, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2018, No. 2, pp. 3–6.
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Ikramov, K.D., Vorontsov, Y.O. Numerical Solution of a Semilinear Matrix Equation of the Stein Type in the Normal Case. MoscowUniv.Comput.Math.Cybern. 42, 51–54 (2018). https://doi.org/10.3103/S0278641918020036
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DOI: https://doi.org/10.3103/S0278641918020036