📅 2024-11-19 — Session: Analysis and Enhancement of Gauss-Seidel Method
🕒 18:30–19:00
🏷️ Labels: Gauss-Seidel, Convergence, Numerical Methods, Python, Algorithm Improvement
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal
The goal of this session was to analyze and enhance the Gauss-Seidel method for solving numerical systems, focusing on convergence issues and implementation improvements.
Key Activities
- Convergence Analysis: Conducted a detailed analysis of the Gauss-Seidel method’s convergence properties, examining the spectral radius of the iteration matrix and its impact on convergence.
- Error Identification: Identified errors in the method’s implementation, particularly in the update of x values and initial conditions.
- Method Improvement: Developed an improved version of the Gauss-Seidel method in Python, enhancing error checking and iteration consistency.
Achievements
- Clarified the relationship between spectral radius and convergence.
- Corrected implementation errors and improved the algorithm’s robustness.
Pending Tasks
- Further testing of the improved implementation with different initial vectors.
- Validation of results against known solutions to ensure accuracy.