The iterative formula of Newton method for solving nonlinear equations is derived.

The iterative formula of Newton method for solving nonlinear equations is derived:1x (n+1) = x (n)-f (x (n))/f' (x (0)).

Newton method, also known as Newton-Raphson method, is an approximate method for solving equations in real number domain and complex number domain proposed by Newton in17th century. Most equations don't have Luda's formula for finding roots, so it is very difficult or even insoluble to find exact roots, so it is particularly important to find approximate roots of equations.

It has been proved that if it is continuous and the zero point of the solution is isolated, then there is a region around the zero point, and Newton's method will converge as long as the initial value is located in this adjacent region. And if it is not 0, Newton's method will have the performance of square convergence. Roughly speaking, this means that the effective number of Newton method results will double with each iteration.

Iterative method, also known as trial and error method, is a process of recursively deriving new values from the old values of variables. Corresponding to iterative method, it is direct method (or one-time solution), that is, one-time solution. Iterative algorithm is the basic method to solve problems with computers. It takes advantage of the computer's fast operation speed and is suitable for repeated operation.

Let the computer execute a set of instructions (or some steps) repeatedly, and every time this set of instructions (or these steps) is executed, a new value is deduced from the initial value of the variable. Among the problems that can be solved by iterative algorithm, at least one variable can directly or indirectly derive new values from old values, and this variable is an iterative variable.

Control the iterative process:

When to end the iterative process is a problem that must be considered when writing iterative programs. We can't let the iterative process go on endlessly. The control of iterative process can usually be divided into: but the number of iterations required is a certain value and can be calculated.

However, the number of iterations required cannot be determined. For the former case, a fixed number of loops can be constructed to control the iterative process; In the latter case, the conditions that can be used to end the iterative process need to be further analyzed by paranuclear vertical analysis.