On projection methods for large-scale Riccati equations

In the numerical solution of the algebraic Riccati equation $A^* X + XA â XBB^â X + C^â C = 0$, where $A$ is large, sparse and stable, and $B$, $C$ have low rank, projection methods have recently emerged as a possible alternative to the more established Newton-Kleinman iteration. A robust implementation of these methods opens to new questions on the use of dissipativity properties of the given matrix $A$. In this talk we briefly discuss the algorithmic aspects of projection methods, together with some new hypotheses that ensure their well posedness. If time allows, considerations on the differential Riccati equation will be included.Non UBCUnreviewedAuthor affiliation: Universita' di BolognaFacult