Scientific

Eigenvalue avoided crossings

Suppose you have a collection of data matrices each of which has the same number of columns. The HO-GSVD can be used to identify common features that are implicit across the collection. It works by identifying a certain (approximate) invariant subspace of a matrix that is a challenging combination of the collection matrices. In describing the computational process I will talk about the Higher Order
CS decomposition and a really weird optimization problem that I bet you have never seen before! Joint work with Orly Alter, Priya Ponnapalli, and Mike Saunders.

Relaxations for some NP-hard problems based on exact subproblems. Joint work with E. Adams, M. Anjos (Montreal) and A. Wiegele (Klagenfurt).

Model Order Reduction Methods for linear systems are well studied and many successful methods exist. We will review some and explain more recent advances in Parametric Model Order Reduction. The focus will be on methods where we interpolate certain signicant measures, that are computed for specic values of the parameter by
Radial Basis Function Interpolation. These measures have a disadvantage as they behave like eigenvalues of matrices depending on parameters and we will explain how that can be dealt with in practice. We will furthermore need to introduce a technique to create a medium size model.

PLQ Modeling and Optimization with applications to machine learning, system identification, and Kalman Smoothing