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Mathematics Colloquium


Date:  Tuesday, March 08, 2011

Title:  Ziwet lectures I: Approximation by rational functions

Abstract:  Rational functions are more powerful than polynomials, but also more fragile. We explain why, and present a new algorithm that gets the best of both worlds. Lecture 2: Wednesday 9th March, 4-5 p.m., 1084 East Hall Title: Impossibility of fast stable approximation of analytic functions from equispaced samples Suppose $f$ is analytic on $[-1,1]$ and you sample it at $n$ equally spaced points. There are excellent algorithms for estimating $f$ between the points. Nevertheless we prove that any algorithm, linear or nonlinear, must fail as $n \to \infty$. Lecture 3: Thursday 10th March, 3-4 p.m., 1360 East Hall Title: Four bugs on a rectangle (Public Lecture) Suppose four bugs at the corners of a $2 \times 1$ rectangle start chasing each other at speed 1. Bug 1 chases bug 2, bug 2 chases bug 3, and so on. What happens next will surprise you. As we follow the bugs to their eventual collision at the center, we will encounter the biggest numbers you've probably ever seen and confront some fundamental questions about what it means to try to understand our world through mathematics.

Speaker:  Nick Trefethen
Institution:  University of Oxford


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