A method is presented to solve the real algebraic Riccati equation -XNX + XA + ATX + K = 0, whereK = KTandN = NT. The solution for the corresponding eigenvalue problemMx = λ x, whereMis a Hamiltonian matrix, is computed by an algorithm similar to the QR algorithm. Special symplectic matrices are used for the transformation ofMsuch that the Hamiltonian form is preserved during the computations.
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Bunse‐Gerstner et al. (1986) studied this question.