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

Ammar, Gregory; Benner, Peter; Mehrmann, Volker

ETNA, Electron. Trans. Numer. Anal. 1, 33-48 (1993).

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)

Keywords:

algorithm; algebraic matrix Riccati equations; linear optimal control; Lagrangian invariant subspace; Hamiltonian matrix