Speaker
Description
Recent contributions for rational approximation include the p-AAA method (and variations) and the extension of the Loewner framework to multiple dimensions. These contributions are recent and are inspiration for further analysis and algorithmic improvements.
In this talk, we combine two ingredients that have proven to be successful in their respective contexts, i.e., the AAA method for univariate rational approximation, and tensor decompositions for the representation of low rank discrete multidimensional data. We present a tensor-based framework for multivariate rational approximation from function samples given on tensor-product grids. The approach combines a low-rank tensor decomposition with the set-valued AAA algorithm. We compare the proposed method against the current state-of-the-art p-AAA by numerical experiments. In particular, we examine both robustness and computational cost on challenging function classes, including nonsmooth and highly oscillatory functions. We also investigate performance in the presence of noise in the sampled data.