Newton's Method: Graphical Approach

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Newton method for systems: Fixed point iterations

Explores the Newton method for systems and fixed point iterations, discussing convergence and properties.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

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 Analysis: Newton's Method

Explores Newton's method for finding roots of nonlinear equations and its interpretation as a second-order method.

Root Finding Methods: Secant, Newton, and Fixed Point Iteration

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.

Newton Method: Convergence and Quadratic Care

Covers the Newton method and its convergence properties near the optimal point.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.

Newton's Method: Convergence and Applications

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