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.
To appear in ACM Transactions on Mathematical Software, Vol 38, No 3. Formerly: Argonne National Laboratory Mathematics and Computer Science Division Preprint ANL/MCS-P1785-0810.