Abstract

Polynomials are among the oldest ideas in mathematics, and they are also one of the most powerful tools for practical computing. Rational functions generalize them in ways that give new power near singularities and on unbounded regions. This four-hour event will blend:

1) THEORY , based on the textbook Approximation Theory and Approximation Practice. Topics touched upon will include the barycentric interpolation formula, the Runge phenomenon, rootfinding via colleague matrices, the Remez algorithm for best approximation, Gauss quadrature, and analytic continuation;

and

2) PRACTICE , using Chebfun. Participants should bring lapops leaded with Matlab and plan to spend some enjoyable time working in pairs on some challenging computational problems, which will touch upon ODEs and PDEs as well as the topics mentioned above. No prior Chebfun experience is needed but you should be comfortable in Matlab.