Newton method

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(also called Newton-Raphson method). This is the iterative scheme to find a zero of a function:


LaTeX: 
x' = x - J(x)^{-1} F(x),


where LaTeX: \textstyle F:\mathbb{R}^n \to \mathbb{R}^n LaTeX: \textstyle (F \in C^1) and LaTeX: J(x) is the jacobian of LaTeX: F (assumed nonsingular). In mathematical programming this is used to find a stationary point, where LaTeX: F=\nabla f and LaTeX: J=H_f. Lacking global convergence, this leads to the modified Newton method, sometimes called the damped Newton method. (See the associated myth, Myth NLP-13 to avoid misconception.)


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