Concept

Newton's method

Related lectures (28)

Newton Method: Convergence Analysis

Explores the Newton method for root finding and its convergence analysis, including the modified Newton method.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Newton's Method: Order 2

Explains Newton's method of order 2 for finding function zeros.

Iterative Methods for Linear Equations

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Convergence of Fixed Point Methods

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

Iterative Methods for Nonlinear Equations

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

Newton's method on Riemannian manifolds

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Newton's Method: Graphical Approach

Illustrates the Newton's method graphically, discussing convergence and extreme cases.

Newton's Method: Convergence Analysis

Explores the convergence analysis of Newton's method for solving nonlinear equations, discussing linear and quadratic convergence properties.

Finite Element Modeling

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

Newton's Method: Fixed Point Iterative Approach

Covers Newton's method for finding zeros of functions through fixed point iteration and discusses convergence properties.

Finite Element Modeling: Dynamics

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

Newton's Method: Optimization & Indefiniteness

Covers Newton's Method for optimization and discusses the caveats of indefiniteness in optimization problems.

Newton's Method for Dynamical Systems

Explores Newton's method for dynamical systems, GMRES, FGMRES, optimization, multishooting, and trust-region methods.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Convergence Analysis: Explicit RK Scheme

Explores the convergence analysis of the Explicit Runge-Kutta scheme for accurate numerical solutions.

Newton's Method: Optimization Techniques

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

Newton Method: Nonlinear Equations

Introduces the Newton method for solving nonlinear equations through iterative processes and practical examples.

Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Linear Systems: Convergence and Methods

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