Rational Functions

Explore the groundbreaking advancements in rational approximation theory and its applications to numerical computation in this 59-minute prize lecture by L. N. Trefethen from Oxford University. Delve into the philosophical and historical aspects of rational functions before focusing on the innovative "AAA" and "lightning" algorithms for solving partial differential equations in complex domains with corner singularities. Gain insights into the work of collaborators Pablo Brubeck, Abi Gopal, Yuji Nakatsukasa, and Olivier Sete. Learn about rational functions in mathematics and numerical analysis, their relationship with polynomials, Triple A representations, the Newman Theorem, root exponential convergence, and Lightning Stoke demos. Conclude with a recap and a thought-provoking discussion on the nature of functions.

Introduction
Rational Functions in Mathematics
Rational Functions in Numerical Analysis
Rational Functions and Polynomials
TripleA
Representations
Triple A
Newman Theorem
Root Exponential Convergence
Lightning Stoke
Demos
Recap
What is a function