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Zeitschrift für Analysis und ihre Anwendungen

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Volume 28, Issue 2, 2009, pp. 205–222
DOI: 10.4171/ZAA/1381

Published online: 2009-06-30

Error Estimates for the Cardinal Spline Interpolation

Gennadi Vainikko[1]

(1) Tartu University, Estonia

For the Sobolev class $W_{\textrm{per}}^{m,\infty}(\mathbb{R})$ of 1-periodic functions, an unimprovable error estimate for the spline interpolants of order $m$ on the uniform grid is known. In the present paper, this error estimate is extended to the Sobolev class $V^{m,\infty}(\mathbb{R})$ of (nonperiodic) functions on $\mathbb{R}$ having bounded $m$th derivative. Some further error estimates are established including the error estimates for derivatives of the spline interpolant.

Keywords: Splines, interpolation, error estimates, best constants

Vainikko Gennadi: Error Estimates for the Cardinal Spline Interpolation. Z. Anal. Anwend. 28 (2009), 205-222. doi: 10.4171/ZAA/1381