Error Bounds on Derivatives during Simulations
Abstract
The methods commonly used for numerical differentiation, such as the "centerdifference formula" and "fourpoints formula" are unusable in simulations or realtime 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 higherorder derivatives. That work did not include a rigorous proof of correctness nor the error bounds. In this paper, the correctness and error bounds of that algorithm are proven, explicit forms are given for the coefficients, and several interesting corollaries are proven.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.0280
 Bibcode:
 2012arXiv1212.0280B
 Keywords:

 Mathematics  Numerical Analysis;
 Computer Science  Computational Engineering;
 Finance;
 and Science;
 65D25;
 65D15;
 68U20;
 68W30;
 68W40
 EPrint:
 Six page paper with five pages of appendices