A MULTISHIFT ALGORITHM FOR THE NUMERICAL SOLUTION OF ALGEBRAIC RICCATI EQUATIONS
Gregory S. Ammar, Peter Benner, Volker Mehrmann · 1993
. We study an algorithm for the numerical solution of algebraic matrix Riccati equations that arise in linear optimal control problems. The algorithmcan 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. Key words. algebraic matrix Riccati equation, Hamiltonian matrix, Lagrangian invariant subspace. AMS subject classifications. 65F15, 15A24, 93B40. 1. Introduction. We consider the numerical solution of algebraic matrix Riccati equations of the form G+A T X +XA \\Gamma XRX = 0; (1) with A; G; R 2 R n;n , and where G and R are symmetric positive semidefinite matrices. These equations arise in linear quadratic optimal control problems, differential games, and Kalman filtering problems. In these applications the s...