Numerical solution of the discrete BHH-equation in the normal case
Kh.D. Ikramov1, Yu.O. Vorontsov2
1Lomonosov Moscow State University, Moscow, Leninskie Gory, 1, Russia, 119899
2LLC В«Globus Media», 1-i Nagatinskii pr-d, d. 10, Moskva
Keywords: непрерывное и дискретное уравнения Сильвестра, BHH-уравнения, форма Шура, сопряженно-нормальная матрица, функция Matlab'а dlyap, continuous- and discrete-time Sylvester equations, BHH-equations, Schur form, conjugate-normal matrix, Matlab function dlyap
Abstract
It is known that the solution of the semilinear matrix equation X - A\overline X 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. We propose a method for solving the original semilinear equation in the normal case that permits to almost halve the execution time for equations of order n = 3000 compared to the library function dlyap, which solves Stein equations in Matlab.
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