Newton's method

English

Etymology

Named after Isaac Newton.

Proper noun

Newton's method

(mathematics) A method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

Usage notes

For the equation ${\\displaystyle f(x)=0}$ , the iteration is ${\\displaystyle x_{n+1}=x_{n}-{\\frac {f(x_{n})}{f'(x_{n})}}}$ , where ${\\displaystyle n=0,1,2,...}$ , and ${\\displaystyle x_{0}}$ is the first approximation to the solution.

Synonyms

Newton-Raphson method

单词	Newton's method
释义	Newton's method English Etymology Named after Isaac Newton. Proper noun Newton's method (mathematics) A method for finding successively better approximations to the roots (or zeroes) of a real-valued function. Usage notes For the equation ${\\displaystyle f(x)=0}$ , the iteration is ${\\displaystyle x_{n+1}=x_{n}-{\\frac {f(x_{n})}{f'(x_{n})}}}$ , where ${\\displaystyle n=0,1,2,...}$ , and ${\\displaystyle x_{0}}$ is the first approximation to the solution. Synonyms Newton-Raphson method
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