Newton's method

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.

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:

单词	Newton Method
释义	Newton Method 英语百科 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 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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Newton Method

Newton's method