Seonglae Chogeneralization to multi-dimension
An n-th degree equation requires n iterations for a meaningful approximation
The reason it's not actually used is complexity, and the Newton-Raphson method works well when the Hessian matrix is positive definite
H is Hessian Matrix
- more few steps and one directional
Generalized form
Newton methods approximations
Newton's method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then
https://en.wikipedia.org/wiki/Newton's_method