BibTeX
@ARTICLE{
         More2014Dyt,
       title = "Do you trust derivatives or differences?",
       journal = "Journal of Computational Physics",
       volume = "273",
       pages = "268--277",
       year = "2014",
       issn = "0021-9991",
       doi = "http://dx.doi.org/10.1016/j.jcp.2014.04.056",
       url = "http://www.sciencedirect.com/science/article/pii/S0021999114003325",
       author = "Jorge J. Mor{\'e} and Stefan M. Wild",
       keywords = "Iterative solvers",
       abstract = "We analyze the relationship between the noise level of a function and the accuracy
         and reliability of derivatives and difference estimates. We derive and empirically validate measures
         of quality for both derivatives and difference estimates. Using these measures, we quantify the
         accuracy of derivatives and differences in terms of the noise level of the function. An interesting
         observation based on these results is that the derivative of a function is not likely to have
         working precision accuracy for functions with modest levels of noise.",
       ad_tools = "ADiMat, INTLAB",
       ad_theotech = "Stability"
}