, Volume 21, Issue 2, pp 151-169

Optimal numerical differentiation usingN function evaluations

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Abstract

An optimal choice ofu for approximating thed th derivative,d=1,2, of a real valued function of a real variable by a difference quotient of the formh d i=1 n w i f(x+u i h) is given. Ifd=1 andn is odd, or ifd=2 andn is even, this choiceu turns out to be surprisingly asymmetric.