Lectures related to Splines: Least-Squares Method

Covers polynomial interpolation and least-squares approximations to minimize errors.

Explores finite dimensional spaces, covering extraction process, bases generation, and space completion.

Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.

Explores the control of complexity in hypothesis spaces and the trade-off between approximation and estimation in risk decomposition.

Explains the Lagrange interpolation method for arbitrary n and constructing polynomials through given points.

Covers numerical integration techniques, focusing on Lagrange interpolation and various quadrature methods for approximating integrals.

Covers the basics of linear regression and how to solve estimation problems using least squares and matrix notation.

Explores challenges in polynomial approximation, stability issues, and error analysis in numerical differentiation.