Error Analysis of Splines for Periodic Problems Using Lattice Designs

Xiaoyan Zeng, King-Tai Leung, Fred J. Hickernell

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review


Splines are minimum-norm approximations to functions that interpolate the given data, (xi, f(xi)). Examples of multidimensional splines are those based on radial basis functions. This paper considers splines of a similar form but where the kernels are not necessarily radially symmetric. The designs, {xi}, considered here are node-sets of integration lattices. Choosing the kernels to be periodic facilitates the computation of the spline and the error analysis. The error of the spline is shown to depend on the smoothness of the function being approximated and the quality of the lattice design. The quality measure for the lattice design is similar, but not equivalent to, traditional quality measures for lattice integration rules.

Original languageEnglish
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2004
EditorsHarald Niederreiter, Denis Talay
PublisherSpringer Berlin Heidelberg
Number of pages14
ISBN (Electronic)9783540311867
ISBN (Print)9783540255413
Publication statusPublished - 6 Dec 2005

User-Defined Keywords

  • spline
  • lattice designs
  • circulant matrix


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