Title: A tangent space splitting method for data assimilation: shadowing and synchronization

Abstract

We start with an introduction to Lyapunov exponents, their computation, and their role in synchronization of chaotic systems and shadowing of hyperbolic systems.  Next we discuss how these ideas can be combined to construct a data assimilation method.  In this method, we iteratively solve for a model trajectory on an assimilation window.  The update is split into its components in the unstable and stable tangent spaces. Newton iteration is applied in the unstable directions, followed by a forward integration to synchronize the unstable directions

Location: KdVI meeting room, Science Park 107, room F3.20.