Convergence theory for the AAA-Lawson algorithm

Prove convergence of the AAA-Lawson iteratively reweighted least-squares algorithm for complex rational minimax approximation under appropriate assumptions, and characterize failure modes.

Background

AAA-Lawson improves AAA near-best fits toward minimax optimality by iterative reweighting, yet the authors explicitly note the lack of a convergence theory and report occasional non-convergence. A convergence analysis would strengthen its reliability near machine precision and in discretely sampled settings.