Adaptive Numerical Differentiation

R. S. Stepleman, N. D. Winarsky
1979 Mathematics of Computation  
It is well known that the calculation of an accurate approximate derivative f'(x) of a nontabular function fix) on a finite-precision computer by the truncation errors cause poor answers, while if ft is too small, cancellation and other "rounding" errors cause poor answers. We will show that by using simple results on the nature of the asymptotic convergence of d(ft) to /', a reliable numerical method can be obtained which can yield efficiently the theoretical maximum number of accurate digits
more » ... of accurate digits for the given machine precision.
doi:10.2307/2006459 fatcat:q6zchlgclfgghmq4txld2wulzu