A structure-preserving method for generalized algebraic Riccati equations based on pencil arithmetic

This paper describes a numerical method for extracting the stable right deflating subspace of a matrix pencil Z − λY using a spectral projection method. It has several advantages compared to other spectral projection methods like the sign function method. In particular it avoids the rounding error induced loss of accuracy associated with matrix inversions. The new algorithm is particularly well adapted to solving continuous time algebraic Riccati equations. In numerical examples, it solves Riccati equations to high accuracy.