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Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations. (English) Zbl 1169.65038

The authors present structured doubling algorithms for the computation of the weakly stabilizing Hermitian solutions of the continuous- and discrete-time algebraic Riccati equations (CARE and DARE), respectively. It is assumed that the partial multiplicities of purely imaginary and unimodular eigenvalues of the associated Hamiltomian and symplectic pencil, respectively, are all even and the C/DARE and the dual C/DARE have weakly stabilizing Hermitian solutions with property (P). Under these assumptions, it is proved that if the algorithms do not break down, they converge to the desired Hermitian solutions globally and linearly. The effectiveness of the algorithms is tested with some numerical experiments.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
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