Explored Numerical Error Mitigation Techniques

📅 2024-08-22 — Session: Explored Numerical Error Mitigation Techniques

🕒 17:00–21:15
🏷️ Labels: Numerical Analysis, Error Propagation, Python, Data Science
📂 Project: Dev
⭐ Priority: MEDIUM

Session Goal: The session aimed to explore various numerical error mitigation techniques in computational contexts, focusing on rounding errors and error propagation using Taylor series.

Key Activities:

1. Error of Rounding and Catastrophic Cancellation: A detailed reflection on the impact of rounding errors and catastrophic cancellation in numerical calculations was conducted. Recommendations were provided to mitigate these errors.
2. Error Propagation with Taylor Series: An exploration of error propagation in multivariable functions using Taylor series approximation was performed. This included practical examples to illustrate how input uncertainties affect final outcomes.
3. Floating Point Precision in Python: Instructions were given on using Python’s decimal.Decimal type to set floating point precision to 16 decimals, with code examples and explanations.
4. Factorial Calculations with NumPy and SciPy: Methods to calculate factorials using NumPy and SciPy were explained, with code examples for single numbers and arrays.

Achievements:

• Clarified the concepts of rounding errors and catastrophic cancellation.
• Developed a comprehensive guide on error propagation using Taylor series.
• Implemented precision settings for floating point numbers in Python.
• Demonstrated factorial calculations using NumPy and SciPy.

Pending Tasks:

• Further exploration of advanced error mitigation techniques in numerical analysis.
• Application of these techniques in real-world data science scenarios.