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An Adaptive MFD Method for the Obstacle Problem Read chapter Read first chapter

2013 | OriginalPaper | Chapter

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

Authors : E. H. Georgoulis, J. Levesley, F. Subhan

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

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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.

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Metadata
Title
Multilevel Sparse Kernel-Based Interpolation Using Conditionally Positive Definite Radial Basis Functions
Authors
E. H. Georgoulis
J. Levesley
F. Subhan
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Numerical Mathematics and Advanced Applications 2011

Print ISBN: 978-3-642-33133-6

Electronic ISBN: 978-3-642-33134-3

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33134-3_17

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