A symplectic QR like algorithm for the solution of the real algebraic Riccati equation
Angelika Bunse‐Gerstner, Volker Mehrmann · IEEE Transactions on Automatic Control · 1986
A method is presented to solve the real algebraic Riccati equation -XNX + XA + A^{T}X + K = 0, whereK = K^{T}andN = N^{T}. The solution for the corresponding eigenvalue problemMx = \lambda 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.