Abstract: | We consider the approximation of the function (x) and its derivative '(x) on a, b] given that (x) C
2, N, i.e., belongs to the class of functions f(x) that satisfy the conditions f (x)![par](/content/t65t47p7r2135842/xxlarge8741.gif) 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.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 57–61, 1985 |