“Newton–Raphson method”的概念、定义、翻译、参考文献-科学参考

Newton–Raphson method

Mathematics

Statistics

An algorithmic method for constructing a sequence of approximations to a root of an equation. Suppose it is desired to solve the equation f(x)=0 and that x₁ is an approximate value for the root of the equation. If we write f′(x_n) for the value of the derivative of f(x) (with respect to x) evaluated at the point x=x_n, the sequence defined by $Newton–Raphson method$ usually converges to a root of the equation. It is based on constructing the tangent to the curve y=f(x) at the point (x_n, f(x_n)), and taking x_n+1 to be the x-coordinate of the point where this tangent cuts the x-axis.

单词	Newton–Raphson method
释义	Newton–Raphson method Mathematics A synonym for Newton’s method. Statistics An algorithmic method for constructing a sequence of approximations to a root of an equation. Suppose it is desired to solve the equation f(x)=0 and that x₁ is an approximate value for the root of the equation. If we write f′(x_n) for the value of the derivative of f(x) (with respect to x) evaluated at the point x=x_n, the sequence defined by $Newton–Raphson method$ usually converges to a root of the equation. It is based on constructing the tangent to the curve y=f(x) at the point (x_n, f(x_n)), and taking x_n+1 to be the x-coordinate of the point where this tangent cuts the x-axis.
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