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A multishift algorithm for the numerical solution of algebraic Riccati equations. (English) Zbl 0809.65040

Summary: We study an algorithm for the numerical solution of algebraic matrix Riccati equations that arise in linear optimal control problems. The algorithm can be considered to be a multishift technique, which uses only orthogonal symplectic similarity transformations to compute a Lagrangian invariant subspace of the associated Hamiltonian matrix. We describe the details of this method and compare it with other numerical methods for the solution of the algebraic Riccati equation.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
93B40 Computational methods in systems theory (MSC2010)
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