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Best approximations of continuous functions by spline functions
An investigation of the approximation on [0, 1] of functionsf (x) by spline functions s(f,ϕ; x) of degree 2r-1 and of deficiency r (r>1) depending on the vector functionϕ =ϕ1 (x),...,ϕr-1(x) andExpand
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Widths of sets of functions of discrete variable
We obtain exact values of Kolmogorov and linear widths of arbitrary dimension for sets of functions of discrete variable with bounded difference of a given order.
Studies on extremal problems of spline-approximation
We give a survey of the most important results on extremal problems of approximation by splines which were obtained by N. P. Korneichuk or stimulated by the methods he developed.
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Optimal interpolation of differentiable periodic functions with bounded higher derivative
The problem of the optimal recovery of functions from the set WMr is considered. It is shown, in particular, that for such recovery the use of information about the values of the function at 2nExpand
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In this paper we obtain precise approximation values in the metrics of C and Lp by interpolating Hermitian splines on a number of classes of differentiable functions.
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Approximation by cubic splines in the classes of continuously differentiable functions
The problem of approximating continuously differentiable periodic functionsf(x) by cubic interpolation splines sn(f; x) with equidistant nodes is considered. Asymptotically exact estimates forExpand
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Accurate estimates of deviations of spline approximations to classes of differentiable functions
We derive the approximation on [0, 1] of functionsf(x) by interpolating spline-functions sr(f; x) of degree 2r+1 and defect r+1 (r=1, 2,...). Exact estimates for ¦f(x)−sr(f; x) ¦ and ∥f(x)−sr(f;Expand
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