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词汇 Newton iteration
分类 英语词汇 英语翻译词典
释义

Newton iteration

中文百科

牛顿法 Newton's method

（重定向自Newton iteration）
蓝线表示方程f而红线表示切线. 可以看出xn+1比xn更靠近f所要求的根x.
The tangent lines of x3 - 2x + 2 at 0 and 1 intersect the x-axis at 1 and 0 respectively, illustrating why Newton's method oscillates between these values for some starting points.

牛顿法（Newton's method）又称为牛顿-拉弗森方法（Newton-Raphson method），它是一种在实数域和复数域上近似求解方程的方法。方法使用函数f(x)的泰勒级数的前面几项来寻找方程f(x)=0的根。

英语百科

Newton's method 牛顿法

（重定向自Newton iteration）
The function ƒ is shown in blue and the tangent line is in red. We see that xn+1 is a better approximation than xn for the root x of the function f.
The tangent lines of x3 - 2x + 2 at 0 and 1 intersect the x-axis at 1 and 0 respectively, illustrating why Newton's method oscillates between these values for some starting points.
Basins of attraction for x5 - 1 = 0; darker means more iterations to converge.
The graph of a strictly concave quadratic function is shown in blue, with its unique maximum shown as a red dot. Below the graph appears the contours of the function: The level sets are nested ellipses.

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

The Newton–Raphson method in one variable is implemented as follows:
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