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Best approximations of continuous functions by spline functions

- V. L. Velikin
- Mathematics
- 1 July 1970

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) and… Expand

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Widths of sets of functions of discrete variable

- Yu. V. Velikina, V. L. Velikin
- Mathematics
- 1 October 1996

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.

Sharp error bounds for certain optimal methods of reconstruction of differentiable periodic functions

- V. L. Velikin
- Mathematics
- 1983

Studies on extremal problems of spline-approximation

- V. L. Velikin, N. A. Nazarenko
- Mathematics
- 1990

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

- V. L. Velikin
- Mathematics
- 1977

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 2n… Expand

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Nikolai Pavlovich Korneichuk (on his seventieth birthday)

- V. P. Motornyi, N. A. Nazarenko, S. M. Nikol'skii, S. Pereverzev, V. Ruban, V. L. Velikin
- Mathematics
- 30 June 1990

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PRECISE APPROXIMATION VALUES BY HERMITIAN SPLINES ON CLASSES OF DIFFERENTIABLE FUNCTIONS

- V. L. Velikin
- Mathematics
- 28 February 1973

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

- V. L. Velikin
- Mathematics
- 1 February 1972

The problem of approximating continuously differentiable periodic functionsf(x) by cubic interpolation splines sn(f; x) with equidistant nodes is considered. Asymptotically exact estimates for… Expand

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Accurate estimates of deviations of spline approximations to classes of differentiable functions

- V. L. Velikin, N. Korneichuk
- Mathematics
- 1 May 1971

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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