# Computational Mathematics and Scientific Computing Seminar

## Numerical Computation with Rational and Harmonic Functions

**Speaker:**
Nick Trefethen, Oxford and NYU Courant

**Location:**
Warren Weaver Hall 1302

**Date:**
Sept. 28, 2018, 10 a.m.

**Synopsis:**

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.