1. Theoretical basis

Understand the mathematical theoretical basis of fixed point problem, including fixed point theorem, Newton method and so on. These basic theories provide mathematical tools and methods for solving fixed point problems.

2. Iterative method

Iterative method is one of the common methods to solve the problem of passing the fixed point. Through iterative calculation, the approximate solution of the fixed point is approached step by step. Common iterative methods include simple iterative method and Newton iterative method.

3. Numerical method

The numerical calculation method can also be used to solve the over-fixed point problem. By transforming the problem into the form of numerical calculation, the approximate solution of the fixed point is obtained by numerical calculation. Common numerical methods include numerical approximation method, difference method and so on.

4. Optimization algorithm

The problem of passing the fixed point can also be regarded as an optimization problem, and the fixed point can be solved by means of optimization algorithm. For example, gradient descent method, genetic algorithm and other optimization algorithms can be used to find the optimal solution of a fixed point.

5. Solve nonlinear equations

The super fixed point problem can be transformed into a nonlinear equation solving problem. Fixed point solutions can be obtained by using dichotomy, Newton method, secant method and other nonlinear equation solving methods.

The significance of the function passing through the fixed point is: no matter what parameters are taken, the point through which the function passes is the fixed point;

If the function f(x)=ax+ 1 passes through the fixed point (0, 1), because no matter what value A takes, the function must pass through the point (0, 1), so the fixed point that the function f(x) passes through is (0,1);

The problem-solving skills of whether a function with parameters has a fixed point;

Find the parameters in the function and determine the coefficient of the parameters in the function, so that the parameter coefficient of the function is 0. If there is a solution, the function containing this parameter must pass through a fixed point, and the coordinates of this point can be found.

Summary: The fixed point problem can be solved by grasping the theoretical basis, using iterative method, numerical method, optimization algorithm or solving nonlinear equations.

Different methods are suitable for different types of over-fixed point problems, and it is necessary to choose the appropriate method to solve them according to the specific situation. At the same time, we should pay attention to convergence and stability when solving fixed-point problems to ensure the accuracy and reliability of the solutions.