Practical algorithms for multivariate rational approximation

We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process efficiently and robustly compute coefficients of approximation. second is based an optimization formulation that allows us include structural constraints approximation (in particular, demanding absence singularities), resulting in a semi-infinite problem we solve using outer approach. results synthetic real-life HEP data, compare quality our with traditional polynomial approximations.