Title of the talk: "Padé-Based Approximation of Univariate Non-Smooth Functions"

Date , Time & Venue: 23 September 2025  at 05 PM on Dept. of Mathematics

Abstract: Many physical and engineering problems give rise to solutions that are inherently non-smooth, featuring discontinuities, shocks, or edges. Classical polynomial approximation techniques often fail in such settings, producing undesirable oscillations known as the Gibbs phenomenon. In this talk, I will present Padé-based rational approximation techniques, with a particular focus on piecewise Padé-Chebyshev type methods, that offer an efficient and accurate way to approximate univariate non-smooth functions. These methods sharply capture singularities without requiring prior knowledge of their location or type, achieve higher-order accuracy in smooth regions, and can be extended to more complex scenarios. I will discuss the theoretical underpinnings, error estimates, and adaptive strategies, as well as numerical results demonstrating the robustness of the proposed approaches.

Towards the end of my talk, I will provide an overview of my ongoing and future research directions. In particular, I will discuss my current work on Graph Neural Networks, which centers on developing robust models capable of addressing distributional shifts in graph data.  

About the Speaker: Dr. Akansha earned her master’s degree in Mathematics and Computing from the Indian Institute of Technology (IIT) Guwahati in 2013, followed by a Ph.D. in Approximation Theory from the Indian Institute of Technology (IIT) Bombay in 2022. Since 2022, she has been working as an Assistant Professor in the Department of Mathematics at Manipal Institute of Technology, Manipal. Her research interests lie at the intersection of mathematical theory and deep learning, with a focus on graph neural networks (GNNs), reliable GNNs, and related areas. She is also expanding her research into the emerging field of generative AI, working with Prof. Wenbin Zhang (Florida International University, USA).

Topic for teaching demo: Fundamental Theorem of Linear Maps (Also known as Rank-Nullity Theorem).