Newton method

From Glossary

Jump to: navigation, search

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

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.)

Personal tools