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Newton–Raphson method
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Newton–Raphson method

Created
Created
2023 Mar 16 2:22
Editor
Editor
Seonglae ChoSeonglae Cho
Creator
Creator
Seonglae ChoSeonglae Cho
Edited
Edited
2024 Nov 26 11:40
Refs
Refs
Convexity
Gradient Descent

generalization to multi-dimension

n차 방정식은 n번 하면 의미있는 approximation
실제로 안쓰는 이유는 복잡하고 Newton-Raphson 방법은 헤시안 행렬이 양의 정부호(positive definite)일 때 잘 작동
H is
Hessian Matrix
notion image
  • more few steps and one directional

Generalized form

 
 
 
 
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
Newton's method
https://en.wikipedia.org/wiki/Newton's_method
 

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Newton–Raphson method
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