Numerical Computation with Rational and Harmonic Functions

Seminar: 
Applied Mathematics
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.