Error Estimates for the Cardinal Spline Interpolation

  • Gennadi Vainikko

    Tartu University, Estonia


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

Cite this article

Gennadi Vainikko, Error Estimates for the Cardinal Spline Interpolation. Z. Anal. Anwend. 28 (2009), no. 2, pp. 205–222

DOI 10.4171/ZAA/1381