Event time:
Wednesday, September 26, 2018 - 7:00pm
Location:
AKW 300
Speaker:
Nick Trefethen
Speaker affiliation:
Oxford and NYU
Event description:
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.