Speaker
Description
The adaptive Anderson-Antoulas (AAA) algorithm is capable of generating highly accurate rational approximations to given data. Though AAA almost always produces an approximation to a given target accuracy, the degree of the resulting rational function may be larger than actually required to meet the accuracy tolerance. In this talk, we introduce the nonlinear least-squares adaptive Anderson-Antoulas (NL-AAA) algorithm, which aims to solve the nonlinear least-squares problem arising in the AAA algorithm, as opposed to the linear approximation solved in AAA. The nonlinear problem is solved efficiently with iteratively reweighed least-squares methods. In addition to better accuracy at lower degrees, solving the nonlinear least-squares problem allows us to guarantee monotonic convergence of the NL-AAA method. Further, we provide an analysis of the gradients of each minimization problem, which gives insight into scenarios where AAA is observed to converge sub optimally. Finally, we test our algorithm on numerical examples including classic function approximation problems and applications to reduced order modeling, a field where attaining high accuracy with minimal degree is required.