Abstract: In this lecture, we will talk about results in approximation theory for polynomial/trignometric interpolation using equispaced and Chebyshev nodes. In particular, we will discuss the Runge phenomenon for polynomial interpolation using equispaced nodes, it's connection to Lesbegue constants, and discuss why Chebyshev interpolation does much better. If time permits, I will also talk about the analog of Chebshev interpolation for a more general class of functions.
Reference material:
Chapters 13-15 of Approximation Theory and approximation practice by Nick Trefethen On interpolation and integration in finite-dimensional spaces - Martinsson, Rokhlin and Tygert.
Please contact crampersad@flatironinstitute.org to join this seminar.