Nonlinear approximation with multivariate rational functions and applications

The PhD will be carried out in the NUMA research section of the Department of Computer Science.

Project

Polynomials are ubiquitous in analysis and scientific computing, while rational functions are equally foundational but relatively unexplored in comparison. Advances in the past five to ten years have resulted in great strides forward both in numerical tools and in applicability of rational functions of a single variable. It is the goal of the project to make another leap forward, by building tools for rational functions of several variables. Solving the strongly nonlinear problem of best approximation using multivariate rational functions is highly challenging and would be transformative across disciplines. The project identifies several paths towards that ambitious goal, each within the joined expertise of the PIs, with progressive levels of complexity. Specific research goals focus on the numerical representation of rational functions, on numerical ...