Numerical solution of special algebraic Riccati equations via an exact line search method

We study the numerical solution of a class of algebraic Riccati equations arising in spectral factorization and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> optimal control problems. This type of matrix Riccati equations differs from the standard type usually considered in linear-quadratic regulator problems in that both the quadratic and constant term are positive semidefinite. We show that the exact line search method derived for the standard "continuous-time" algebraic Riccati equation can be applied to this type of equation as well. The method can either be used to solve the Riccati equation iteratively or to improve a solution computed by any other method via iterative refinement.