Inequalities for the derivatives

1999/11/25 by А. Г. Рамм, Ramm, A. G. · 1 citation
Mathematics · #65D25 #65M10 #Advanced Optimization Algorithms Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math-ph/9911034

openalex publication_date 1999/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• On inequalities between norms of partial derivatives on convex domains

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