Lectures related to Newton's Method for Dynamical Systems

Mathematics of Data: Computation Role

Explores the role of computation in data mathematics, focusing on iterative methods, optimization, estimators, and descent principles.

Nonlinear Optimization

Covers line search, Newton's method, BFGS, and conjugate gradient in nonlinear optimization.

TR global convergence (end) + CG

Covers the trust-region method and introduces the truncated conjugate gradients method.

Gradient Descent

Covers the concept of gradient descent in scalar cases, focusing on finding the minimum of a function by iteratively moving in the direction of the negative gradient.

Numerical Methods for Physics: Iterative Solutions and Mesh Convergence

Explores finite differences for solving linear systems from PDEs iteratively, emphasizing convergence criteria and exercises on singularities.

Convergence Analysis: Iterative Methods

Covers the convergence analysis of iterative methods and the conditions for convergence.

Newton's Method: Convergence and Applications

Covers the convergence of Newton's method and its applications in numerical analysis.