Volume 1, pp. 33-48, 1993.

A multishift algorithm for the numerical solution of algebraic Riccati equations

Gregory Ammar, Peter Benner, and Volker Mehrmann

Abstract

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.

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Key words

algebraic matrix Riccati equation, Hamiltonian matrix, Lagrangian invariant subspace.

AMS subject classifications

65F15, 15A24, 93B40.

ETNA articles which cite this article

Vol. 8 (1999), pp. 115-126 Peter Benner, Volker Mehrmann, and Hongguo Xu: A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems

Vol. 26 (2007), pp. 121-145 H. Faßbender: The parametrized $SR$ algorithm for Hamiltonian matrices

Vol. 62 (2024), pp. 95-118 Jens Saak and Steffen W. R. Werner: Using $LDL^T$ factorizations in Newton's method for solving general large-scale algebraic Riccati equations

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