π 2024-09-19 β Session: Developed LU Decomposition with Pivoting
π 16:45β18:00
π·οΈ Labels: Lu Decomposition, Python, Numerical Stability, Error Handling, Matrix Operations
π Project: Dev
β Priority: MEDIUM
Session Goal
The goal of this session was to implement and refine LU decomposition algorithms in Python, focusing on numerical stability and error handling.
Key Activities
- Developed a non-destructive version of Gaussian Elimination using Python and NumPy.
- Implemented LU decomposition steps, including matrix inversion and solving systems of equations.
- Refactored code for execution in Jupyter notebooks.
- Enhanced LU decomposition with partial and full pivoting to improve numerical stability.
- Addressed common errors such as βsingular matrixβ and
UFuncTypeError
by improving error handling and type casting.
Achievements
- Successfully implemented LU decomposition with both partial and full pivoting.
- Improved algorithm stability and error handling.
- Provided complete code examples and detailed explanations for each step.
Pending Tasks
- Further testing and optimization of the LU decomposition algorithm for large matrices.
- Exploration of additional numerical methods to enhance performance.