📅 2024-09-19 — Session: Developed LU Decomposition with Enhanced Pivoting
🕒 16:50–17:50
🏷️ Labels: Lu Decomposition, Python, Numerical Methods, Error Handling
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal
The session aimed to enhance the LU decomposition algorithm by implementing partial and full pivoting techniques to improve numerical stability and handle errors effectively.
Key Activities
- Developed a non-destructive version of Gaussian Elimination using Python and NumPy, focusing on creating new matrices instead of overwriting existing ones.
- Implemented LU decomposition steps and detailed the process of achieving LU decomposition, including the calculation of lower and upper triangular matrices.
- Refactored code for Jupyter notebooks to facilitate execution by removing the
main()function and directly executing code cells. - Enhanced LU decomposition with partial pivoting to prevent division by zero, addressing numerical stability issues.
- Implemented full pivoting for input-output models, ensuring structural integrity during decomposition.
- Addressed and fixed errors such as ‘LinAlgError: singular matrix’ and
UFuncTypeErrorby updating code examples and handling data types appropriately.
Achievements
- Successfully implemented LU decomposition with both partial and full pivoting, enhancing numerical stability and error handling.
- Developed a comprehensive Python implementation for LU decomposition with detailed docstrings and code examples.
Pending Tasks
- Further testing and validation of the LU decomposition implementation in various economic models to ensure robustness and accuracy.