Newton Method: Nonlinear Equations

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Nonlinear Equations: Methods and Convergence

Explores high-order fixed-point methods and Newton-Raphson method for solving nonlinear equations.

Convergence of Fixed Point Methods

Explores the convergence of fixed point methods and the implications of different convergence rates.

The Conjugate Gradients Method (CG)

Covers the Conjugate Gradients method for solving linear systems iteratively with quadratic convergence and emphasizes the importance of linear independence among conjugate directions.

Iterative Methods: Error Control and Linear Systems Resolution

Explores iterative methods for solving linear systems with a focus on error control.

Trust region methods: framework & algorithms

Covers trust region methods, focusing on the framework and algorithms.

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Computing the Newton Step: GD as a Matrix-Free Way

Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.

Iterative Methods for Nonlinear Equations

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Linear Systems: Iterative Methods

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.