For the Sobolev class of 1-periodic functions, an unimprovable error estimate for the spline interpolants of order on the uniform grid is known. In the present paper, this error estimate is extended to the Sobolev class of (nonperiodic) functions on having bounded th 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. 205–222DOI 10.4171/ZAA/1381