Mathematics - Root Finding, Detection and Classification of Multiplicities

Building on my previous work on the classification and isolation of real roots in nonlinear equations, I am now exploring the next stage of the problem: root multiplicity classification. The goal is to investigate new mathematical and computational methods for determining and classifying the multiplicity of isolated roots, beyond conventional derivative-based approaches.

I am looking to collaborate with researchers and students interested in numerical analysis, computational mathematics, nonlinear equations, and scientific computing. If this area aligns with your research interests, I would be happy to connect and discuss potential collaborations.

The main research question is : Can root multiplicity be classified from the local behavior of a function without relying solely on higher-order derivatives?