Publications
J. J. More and S. M. Wild, "Do You Trust Derivatives or Differences?*," Preprint ANL/MCS-P2067-0312, March 2012. [pdf]
We analyze the relationship between the noise level of a function and the accuracy and reliability of derivatives and diff erence estimates. We derive and empirically validate measures of quality for both derivatives and diff erence estimates. Using these measures, we quantify the accuracy of derivatives and diff erences in terms of the noise level of the function. An interesting consequence of these results is that the derivative of a function is not likely to have working precision accuracy for functions with modest levels of noise.
