Professor Nick Trefethen
University of Oxford
Title: "Numerical computation with rational and harmonic functions" at the Applied Mathematics Colloquium.
Abstract: Numerical algorithms are based on approximation of functions. Polynomials can only approximate smooth functions effectively, but rational functions can approximate functions with singularities with fast *root-exponential convergence*: convergence at a rate exp(-C*sqrt(n)), C>0. This property has rarely been exploited. We show how powerful it can be, for example, for solving the Laplace equation on a polygon. An important advance along the way has been the "AAA algorithm" developed with Nakatsukasa and Sete.
Biography: Professor Nick Trefethen is a Professor of Numerical Analysis and the head of the Numerical Analysis Group at the University of Oxford, as well as a Global Distinguished Professor at NYU. Nick was the first winner of the Leslie Fox Prize for Numerical Analysis in 1985, won the Gold Medal of the Institute of Mathematics and its Applications in 2010, and the Naylor Prize and Lectureship in Applied Mathematics from the London Mathematical Society in 2013. He is a fellow of the American Mathematical Society, a member of the National Academy of Engineering in the US, and a Fellow of the Royal Society in the UK.
Host: Hadrien Montanelli & Qiang Du
