Speaker
Description
We discuss analytical estimates for greedy construction of rational approximations, where the underlying function is the linear sketch of an operator resolvent. The canonical example of this setup is the transfer function of a linear dynamical system. Under a sectorial assumption for the operator, this analysis immediately reveals corresponding algorithms, and provides explicit estimates of transfer function rational approximability. The theoretical constructions correspond to explicit Galerkin projection-based reduced order models of the original system, and additionally provide concrete estimates of Hankel singular value decay. The framework we discuss is a paradigm that forges concrete relationships between rational approximation, Kolmogorov n-widths, and Galerkin projection-based model reduction. We will discuss extensions to parametric systems, where this corresponds to multivariate rational approximation through a greedy approach. Finally, we will identify algorithmic challenges and opportunities, investigating numerical procedures that improve on stability and accuracy of the procedure.