Cubic Splines and Least-Squares Approximation

This lecture covers the concepts of cubic splines and least-squares approximation. It starts by defining spline interpolation and then delves into the computation of derivatives. The lecture explains how to interpolate data using splines, focusing on natural splines and the 'not-a-knot' condition. It also discusses the error analysis and the theorem related to least-squares approximation. The instructor demonstrates the application of these concepts through examples and explains the conditions for successful interpolation.