 
Summary: Electronic Transactions on Numerical Analysis
Volume 1, pp. 3348, September 1993
Copyright 1993, Kent State University
ETNA
Kent State University
etna@mcs.kent.edu
A MULTISHIFT ALGORITHM FOR THE NUMERICAL SOLUTION
OF ALGEBRAIC RICCATI EQUATIONS \Lambda
GREGORY AMMAR y , PETER BENNER z , AND VOLKER MEHRMANN x
Abstract. We study an algorithm for the numerical solution of algebraic matrix Riccati equa
tions 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 sub
space.
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;
