• Corpus ID: 12409098

Error Bounds on Derivatives during Simulations

@article{Bard2012ErrorBO,
  title={Error Bounds on Derivatives during Simulations},
  author={Gregory V. Bard and Alexander Basyrov},
  journal={ArXiv},
  year={2012},
  volume={abs/1212.0280}
}
The methods commonly used for numerical differentiation, such as the "center-difference formula" and "four-points formula" are unusable in simulations or real-time data analysis because they require knowledge of the future. In Bard'11, an algorithm was shown that generates formulas that require knowledge only of the past and present values of $f(t)$ to estimate $f'(t)$. Furthermore, the algorithm can handle irregularly spaced data and higher-order derivatives. That work did not include a… 

References

Numerically Estimating Derivatives During Simulations

This research began as an inquiry to discover similar formulas usable when only the past and present, but not the future, are known, and the author uncovered an extremely obscure corner of numerical analysis, where solutions to these dilemmas are feasible.