Mathematical Modeling Learning Notes (ten common algorithms in modeling)

Ten common algorithms in mathematical modeling

1. Monte Carlo Method:

Also called the computer Randomness simulation method, is called the statistical experiment method. Simulations can be used to verify the correctness of their models.

2 data fitting, parameter estimation, interpolation and other data processing

There is often a lot of data to be dealt with in the game, and the key to the data processing is that these methods, usually using MATLAB assistance, can also handle a lot of fitting problems when combined with graphics.

3. Planning for class problem algorithms:

Including linear programming, integer programming, multi-programming, two-time planning, and so on; In the competition, many problems are related to the planning, so many models can be attributed to a set of inequalities as constraints, and several function expressions as the objective function problems, and the solution is the key.

This kind of problem can be solved by lingo software generally.

4. Graph theory Questions:

This paper mainly investigates the algorithm of this kind of problem, including: Dijkstra, Floyd, Prime, Bellman-ford, maximum flow, binary matching and so on. It should be easy for people who are familiar with ACM.

5. Problems in the design of computer algorithms:

The algorithm design includes: Dynamic programming, backtracking search, divide and conquer, branch and bound method (solving integer solution) and so on.

6. Three non-classical algorithms for Optimization theory:

A) Simulated annealing method (SA)

b) Neural Network (NN)

c) Genetic algorithm (GA)

I don't understand,,,

7. Grid algorithm and exhaustive algorithm

8. Methods for discretization of continuous problems

Because the computer can only deal with the problem of discretization, but the actual data is mostly continuous, so the need to discretization of the continuous problem after the computer solution.

such as: differential substitution of differential, summation and other ideas are the common method of discretization of continuous problems.

9. Numerical Analysis method

This paper mainly studies the numerical methods of solving mathematical problems, especially the methods and algorithms applicable to computer implementation.

Include: numerical approximation of function, numerical differential and numerical integration, numerical solution of nonlinear return, numerical algebra, numerical solution of ordinary differential equation, etc.

The main application of MATLAB to solve.

10. Image processing algorithm

This part mainly uses MATLAB to carry on the image processing.

Including display pictures, problem solving instructions and so on.

Mathematical Modeling Learning Notes (ten common algorithms in modeling)