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What (who) is Newton-Raphson - definition

ALGORITHM FOR FINDING A ZERO OF A FUNCTION

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Newton-Raphson iteration

<algorithm> An iterative algorithm for solving equations. Given an equation, f x = 0 and an initial approximation, x(0), a better approximation is given by: x(i+1) = x(i) - f(x(i)) / f'(x(i)) where f'(x) is the first derivative of f, df/dx. Newton-Raphson iteration is an example of an {anytime algorithm} in that each approximation is no worse than the previous one. (2007-06-19)

Newton's method

Newton-Raphson

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 defined for a real variable , the function's derivative , and an initial guess for a root of .

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

Wikipedia

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

x_{1}=x_{0}-{\frac {f(x_{0})}{f'(x_{0})}}

is a better approximation of the root than x₀. Geometrically, (x₁, 0) is the intersection of the x-axis and the tangent of the graph of f at (x₀, f(x₀)): that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as

x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}

until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions and to systems of equations.

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