Cheat Sheet: Choosing the Right Method#
This cheat sheet provides practical guidance for choosing a numerical differentiation strategy in DerivKit based on the characteristics of the function being differentiated.
It is intended as a quick reference rather than a strict decision rule; in practice, multiple methods may be worth trying for difficult cases.
Situation |
Recommended method |
Why |
|---|---|---|
Smooth, cheap function |
Finite differences |
Fast and accurate for smooth functions |
Slightly noisy function |
Ridders finite differences |
Richardson extrapolation improves stability over simple finite differences |
Moderate or structured noise |
Local polynomial fit |
Local regression smooths noise better than finite differences |
High noise / messy signal |
Adaptive polynomial fit (Chebyshev) |
Robust trimming, Chebyshev grid, and fit diagnostics |
Expensive function |
Adaptive polynomial fit (Chebyshev) |
Achieves stable derivatives with fewer function evaluations near |
Need robustness and diagnostics |
Adaptive polynomial fit (Chebyshev) |
Provides fit quality metrics, degree adjustment, and suggestions |
Unsure / first attempt |
Local polynomial fit |
Good default when function behavior is not well known |