Lectures related to Descent methods and line search: Quadratic interpolation

Covers the Newton method for finding zeros of functions using data interpolation.

Covers the derivation of the equation of motion, interpolation, Newton's equation, and energy conservation in finite element modeling.

Introduces the basics of finite element modeling for dynamics and discusses the Newmark method for time integration.

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Covers the basics of Newton interpolation and interpolation polynomials using Lagrange and Newton methods.

Explores trigonometric interpolation for approximating periodic functions and signals using equally spaced nodes.

Introduces nonlinear equations and polynomial interpolation for curve fitting.

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Explores double descent curves and overparametrization in machine learning models, highlighting the risks and benefits.

Covers coordinate descent, a method for optimizing functions by updating one coordinate at a time.

Covers Lagrange interpolation using intervals to find accurate polynomial approximations.

Explores interpolation of regular functions, error analysis, convergence, and Chebyshev polynomials.

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Covers the Finite Element Method, discussing the derivation of the equation of motion and exploring mass and stiffness matrices.

Explores signal reconstruction techniques, including polynomial interpolation challenges and the importance of interpolation functions.

Explores systems of non-linear equations and polynomial interpolation, including the Newton method and Vandermonde matrix construction.

Covers the least squares method for approximating data and handling errors.

Covers advanced numerical analysis topics including deep neural networks and optimization methods.

Covers the optimization of error in polynomial interpolation, focusing on minimizing the error by strategically placing interpolation points.

Explores optimization techniques like gradient descent, line search, and Newton's method for efficient problem-solving.