Analysis Seminar: Wolfgang Erb

November 9, 2016 @ 3:30 pm – 4:30 pm

Title: Is polynomial interpolation really that bad?

Abstract: A myth in numerical analysis (according to a nice article of N. Trefethen) is the belief that polynomial interpolation has to be avoided in practice since it is not stable and converges in general badly to the interpolated function.

In this talk, we are going to shed light on this myth by considering different aspects of polynomial interpolation as numerical stability and convergence properties. We will discuss some ot the theories of Trefethen why polynomial interpolation has such a bad reputation. At the end of the talk, I will give some examples how Chebyshev polynomials can be used efficiently to interpolate data points on Lissajous curves.