JournalszaaVol. 28 , No. 2DOI 10.4171/zaa/1381

Error Estimates for the Cardinal Spline Interpolation

  • Gennadi Vainikko

    Tartu University, Estonia
Error Estimates for the Cardinal Spline Interpolation cover

Abstract

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.