πŸ“… 2024-09-19 β€” Session: Developed LU Decomposition with Pivoting

πŸ•’ 16:45–18:00
🏷️ Labels: Lu Decomposition, Python, Numerical Stability, Error Handling, Matrix Operations
πŸ“‚ Project: Dev
⭐ 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 β€˜singular matrix’ 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.