FastAAA: A fast rational-function fitter

Abstract

FastAAA is an algorithm for fitting rational-functions to a set of N data samples. In each step of the algorithm, it computes an order n fit via a fast, O(Nn), update of the previous order n − 1 fit. The algorithm stops at the first order that yields an acceptable error. The errors of the fits of orders 1… n, are evaluated in O(Nn2) operations. If the data can be represented exactly with n poles, the algorithm is guaranteed to stop after n iterations (in exact arithmetic). It is possible to fit p rational-functions, sharing the same set of poles, to p sets of data, in O(pNn2) operations. The stability of the poles and Hermitian symmetry of the fit can be guaranteed.