Abstract
We consider the approximation of the function ϕ(x) and its derivative ϕ'(x) on [a, b] given that ϕ(x)∈C 2,αN, i.e., belongs to the class of functions f(x) that satisfy the conditions ∥f″(x)∥≤L, f(xi)=yi, i=1,⋯,N, where L and yi are given real numbers and xi are the nodes of an arbitrary grid, a=x1<x2<⋯<XN=b. A solution algorithm on the class of functions C2,L,N is proposed which has optimal accuracy with a constant not exceeding 2. A bound on the approximation error of the function and its derivative is derived.
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 57–61, 1985
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Berezovskii, A.I., Nechiporenko, N.E. Optimal accuracy approximation of functions and their derivatives. J Math Sci 54, 799–803 (1991). https://doi.org/10.1007/BF01097590
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DOI: https://doi.org/10.1007/BF01097590