This article is cited in 1 paper

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

V. L. Velikin, N. P. Korneichuk

Dnepropetrovsk State University

Abstract: We derive the approximation on $[0,1]$ of functions $f(x)$ by interpolating spline-functions $s_r(f;x)$ of degree $2r+1$ and defect $r+1$ ($r=1,2,\dots$). Exact estimates for $|f(x)-s_r(f;x)|$ and $\|f(x)-s_r(f;x)\|_C$ on the class $W^mH_\omega$ for $m=1$, $r=1,2,\dots$ and $m=2,3$, $r=2$ for the case of convex $\omega(t)$, are derived.

UDC: 517.5

Received: 06.04.1970

 English version: Mathematical Notes, 1971, 9:5, 278–284

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