Error Analysis of Splines for Periodic Problems Using Lattice Designs

Xiaoyan Zeng (), King-Tai Leung () and Fred J. Hickernell ()
Additional contact information
Xiaoyan Zeng: Hong Kong Baptist University, Department of Mathematics
King-Tai Leung: Hong Kong Baptist University, Department of Mathematics
Fred J. Hickernell: Hong Kong Baptist University, Department of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 501-514 from Springer

Abstract: Summary 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.

Keywords: spline; lattice designs; circulant matrix (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_31

Ordering information: This item can be ordered from
http://www.springer.com/9783540311867

DOI: 10.1007/3-540-31186-6_31

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().