Newton's Method

Newton's methodIt is a method for approximately solving equations in the real and complex fields, which uses the Taylor series of the function f(x) to calculate the roots of the equation f(y) = 0.

Newton's law

Newton's method uses the first-order and second-order derivatives at the iteration point to approximate the objective function as a quadratic function, then uses the minimum point of the model as a new iteration point, and repeats this process until an approximate minimum value that satisfies the accuracy is obtained.

Characteristics of Newton's method

The speed is relatively fast and highly close to the optimal value.

Newton's method iteration steps

To solve the problem, the iterative algorithm needs to meet the following three points:

• Determine the iterative variable: In a problem that can be solved by an iterative algorithm, there is at least one variable whose new value can be derived from the old value;
• Establishing an iterative relationship: This can usually be done by recursion or reverse deduction;
• Control the iterative process: The required number of iterations is a fixed value, which can be achieved by constructing a fixed number of loops; the required number of iterations is uncertain, and further analysis is needed to derive the conditions for ending the iterative process.

Newton's method classification

• Basic Newton's method
• Global Newton's method