Numerical minimal GAD computation

In this talk, we address Generalized Additive Decompositions (GADs) of symmetric tensors, which constitute a natural generalization of the classical Waring decompositions of forms. We adopt an operatorial perspective by associating each GAD with a dual polynomial-exponential differential series that encodes its geometric nature. In particular, we show how the GAD-size can be measured via the associated inverse system, which can be canonically computed using only linear algebra operations. We then recall the construction of the corresponding Hankel operator and explain how it can be exploited to effectively recover GADs of minimal size under suitable regularity assumptions. Building on this framework, we present a numerical implementation of the method and highlight its improvements over existing approaches within the same regularity regime. Finally, we analyze the numerical stability of the algorithm, demonstrating its robustness when the input tensor is perturbed within a neighborhood of certain osculating varieties of the Veronese variety. This talk is based on the recent preprint arXiv:2510.25681 and reports on joint work with B. Mourrain.