Title: Polynomial/Trigonometric interpolation and beyond
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.
Chapters 13-15 of Approximation Theory and approximation practice by Nick Trefethen
On interpolation and integration in finite-dimensional spaces – Martinsson, Rokhlin and Tygert.