Challenges, Opportunities, and New Horizons in Rational Approximation (25w5376)

The Banff International Research Station will host the “Challenges, Opportunities, and New Horizons in Rational Approximation” workshop in Banff from April 6 - 11, 2025.

A central component of modern scientific investigation involves the approximation of models, data, and signals with functions. In many core computational tasks, we approximate complex or unknown functions with simpler ones that supply highly accurate representations, but are also efficient for computing with. Methods based on rational functions are among the most powerful and promising tools we have for such tasks. In particular, they are effective as a means for efficiently and accurately capturing features associated with complicated phenomena, including pulses, shocks, fragmenting, change points, and impulsive behavior (as in an electrocardiogram). Classical methods, such as Fourier analysis or polynomial interpolation, can struggle in such regimes.

While the practical benefits of implementing computational methods based on rational functions are substantial, new theoretical, algorithmic and software-based developments are needed to make these benefits broadly realizable across diverse scientific communities. This workshop brings together domain scientists, theoreticians, and numerical analysts to further the field of rational approximation---to develop novel algorithms, disseminate recent results, understand the needs of key scientific applications, and identify key challenges for the research community to tackle. This workshop will also produce artifacts to aid researchers working on rational approximation as no comprehensive treatments currently exist.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta’s Advanced Education and Technology.