We employ recent work on computational noise to obtain near-optimal finite difference estimates of the derivatives of a noisy function. Our analysis employs a stochastic model of the noise without assuming a specific form of distribution. We use this model to derive theoretical bounds for the errors in the difference estimates and obtain an easily computable difference parameter that is provably near-optimal. Numerical results closely resemble the theory and show that we obtain accurate derivative estimates even when the noisy function is deterministic.

%B ACM Transactions on Mathematical Software (TOMS) %V 38 %8 08/2010 %G eng %U http://dl.acm.org/citation.cfm?id=2168777&CFID=227501898&CFTOKEN=82333717 %N 3 %1 http://www.mcs.anl.gov/papers/P1785.pdf