Theoretical accuracy guarantees for AAA-computed poles and zeros

Establish rigorous theoretical guarantees for the accuracy of poles and zeros computed from AAA approximants, quantifying how numerical backward stability translates to forward accuracy of the rational function’s singularities and zeros.

Background

AAA determines poles and zeros of the final approximant via a generalized eigenvalue problem, and the computation is backward stable. However, the authors explicitly acknowledge no known theoretical guarantees linking this backward stability to the forward accuracy of the poles and zeros of the rational approximation r(z). A theory would clarify reliability in applications (e.g., singularity detection, resonances, and spectral methods).