Inequalities for the derivatives

Details Inequalities for the derivatives Inequalities for the derivatives

1999-11-25

arxiv.org/abs/math-ph/9911034v1

Physics

Mathematical Physics

Scientific paper

It is proved that one cannot approximate stably the first derivative of a smooth function given noisy values of this function and a bound on this function and its first derivative. Such an approximation is shown to be possible if an a priori bound is known for a fractional derivative of order greater than one. An algorithm is proposed for such a stable approximation and error estimates for the proposed algorithm are given. Under certain assumptions it is proved that this algorithm is best possible among all linear and nonlinear algorithms.

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