Numerical Solution of the Discrete BHH-Equation in the Normal Case
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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.
Keywordscontinuous- and discrete-time Sylvester equations BHH-equations Schur form conjugate-normal matrix Matlab function dlyap
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