https://github.com/nickklos10/cot-4500-as4
Numerical methods for solving systems of linear equations
https://github.com/nickklos10/cot-4500-as4
direct-solution gauss-seidel-method iterative-refinement jacobi-method sor-method
Last synced: 2 months ago
JSON representation
Numerical methods for solving systems of linear equations
- Host: GitHub
- URL: https://github.com/nickklos10/cot-4500-as4
- Owner: nickklos10
- Created: 2024-04-18T00:56:04.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2024-04-18T01:52:29.000Z (about 1 year ago)
- Last Synced: 2025-01-18T02:27:56.531Z (4 months ago)
- Topics: direct-solution, gauss-seidel-method, iterative-refinement, jacobi-method, sor-method
- Language: Python
- Homepage:
- Size: 7.81 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# Numerical Methods for Linear Systems
### Overview
This Python script implements several numerical methods for solving systems of linear equations. It provides implementations for the Jacobi Method, Gauss-Seidel Method, Successive Over-Relaxation (SOR) Method, and Iterative Refinement Method. Additionally, the script includes a direct solution using NumPy's linear solver for comparison purposes.
### Methods Implemented
- **Jacobi Method:** An iterative technique for solving the diagonal entries of a matrix equation.
- **Gauss-Seidel Method:** An improved version of the Jacobi Method that uses the latest updated values for convergence.
- **SOR Method:** Extends the Gauss-Seidel method by using a relaxation factor to potentially accelerate the convergence.
- **Iterative Refinement Method:** Refines a given solution by iteratively correcting the residual error.
- **Direct Solution (for verification and not asked in the assignment):** Uses NumPy's linalg.solve function to compute the exact solution, providing a benchmark for verifying the iterative solutions.
### Requirements
Requirements will be found in the requirements.txt file in the repository
### Usage
To use the script, ensure that Python 3 and NumPy are installed on your system. You can run the script from the command line as follows:
python main.py
### Output
The results are saved to numerical_methods_output.txt in the same directory as the script. The output file will contain the results for each method, formatted clearly for easy comparison.
### Conclusion
This script is useful for educational purposes to understand different iterative methods for solving linear systems and for verifying the convergence and accuracy of these methods against a direct solution.