📅 2024-12-08 — Session: Analyzed Gauss-Seidel Method for Matrix A with Alpha Zero
🕒 15:05–15:15
🏷️ Labels: Matrix Analysis, Gauss-Seidel, Linear Algebra, Convergence, Error Handling
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal
The session aimed to analyze the matrix A when ( \alpha = 0 ) and apply the Gauss-Seidel method for solving the equation ( Ax = b ).
Key Activities
- Conducted matrix analysis to determine the characteristic polynomial and eigenvalues of matrix A.
- Explored the implications of diagonal dominance on the convergence of the Gauss-Seidel method.
- Computed the iteration matrix for the Gauss-Seidel method, including matrix decomposition and spectral radius calculation.
- Addressed error handling and implemented a retry mechanism for computational errors.
- Recomputed the Gauss-Seidel iteration matrix due to previous processing issues.
Achievements
- Confirmed that strict diagonal dominance is not satisfied, affecting convergence guarantees.
- Successfully calculated the spectral radius of the iteration matrix.
Pending Tasks
- Further refine the computation process and clarify manual calculations for improved accuracy and efficiency.