Polynomial Interpolation: Lagrange and Runge Phenomenon

This lecture covers polynomial interpolation, focusing on Lagrange interpolation and the Runge phenomenon. The instructor explains the challenges of polynomial interpolation, such as badly conditioned matrices and the difficulty of solving systems correctly. Different methods for constructing interpolating polynomials are discussed, including the use of Vandermonde matrices. The lecture also delves into the definition of Lagrange polynomials and their associated nodes. Examples of polynomial fitting with varying degrees are presented, showcasing the impact of degree choice on the accuracy of the interpolation.