Multilevel Sparse Kernel-Based Interpolation Using Conditionally Positive Definite Radial Basis Functions

E. H. Georgoulis (), J. Levesley () and F. Subhan ()
Additional contact information
E. H. Georgoulis: University of Leicester, Department of Mathematics
J. Levesley: University of Leicester, Department of Mathematics
F. Subhan: University of Leicester, Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 157-164 from Springer

Abstract: Abstract A multilevel sparse kernel-based interpolation (MLSKI) method, suitable for moderately high-dimensional function interpolation problems has been recently proposed in (Georgoulis et al. Multilevel sparse kernel-based interpolation, submitted for publication). The method uses both level-wise and direction-wise multilevel decomposition of structured or mildly unstructured interpolation data sites in conjunction with the application of kernel-based interpolants with different scaling in each direction. The multilevel interpolation algorithm is based on a hierarchical decomposition of the data sites, whereby at each level the detail is added to the interpolant by interpolating the resulting residual of the previous level. On each level, anisotropic radial basis functions (RBFs) are used for solving a number of small interpolation problems, which are subsequently linearly combined to produce the interpolant. Here, we investigate the use of conditionally positive definite RBFs within the MLSKI setting, thus extending the results from (Georgoulis et al. Multilevel sparse kernel-based interpolation, submitted for publication), where (strictly) positive definite RBFs are used only.

Keywords: Radial Basis Functions (RBFs); Positive Definite Radial Basis Functions; Interpolation Problem; Georgoulis; Site Data (search for similar items in EconPapers)
Date: 2013
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:978-3-642-33134-3_17

Ordering information: This item can be ordered from
http://www.springer.com/9783642331343

DOI: 10.1007/978-3-642-33134-3_17

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 ().