Solving large hollow systems

Overview

This project is a C++ implementation of several mathematical techniques for solving large hollow systems, including:

• Cholesky Decomposition
• Relaxation Method
• LU Decomposition
• Jacobi Method

These techniques can be used to analyze and model the behavior of large hollow systems, and to develop numerical methods for simulating and predicting their behavior. Usage

The program can be executed by providing the size of Laplacian matrix (n,m) and then the program will calculate the decompositions and methods.

To run the program, you will need a C++ compiler. Once you have one installed, you can use the following command to compile the program:

make

And then you can execute the program by running:

./projet

Features

• Cholesky Decomposition : It is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, such as Monte Carlo simulations.
• Relaxation Method: It is a method for solving systems of linear equations.
• LU Decomposition : It is a decomposition of a matrix into a lower triangular matrix L and an upper triangular matrix U.
• Jacobi Method: It is an iterative method for solving systems of linear equations.

Conclusion

This project provides a solid foundation for solving large hollow systems using mathematical techniques in C++. It can be a great starting point for further development in this area.

Note

This is a sample README.md and the program may require further modification and testing before being used in a production environment.