We will review the theory of "fast growing" polynomials and show how to construct them numerically using the (exterior) conformal mapping. We will expand analytic functions in series of fast growing polynomials and show how to use these expansions to con struct the (near) best uniform approximation of these analytic functions on a given curve in the complex plane. We will then concentrate on the function f(z) = 1 z and show how the near best approximation is used for the purpose of matrix preconditioning. Numerical experiments will then be presented.

Pizza and soda will be served for those attending!