Solving large generalized interpolation problems efficiently

Wendland, Holger (2004) Solving large generalized interpolation problems efficiently. In: Neamtu, M and Saff, E (eds.) Advances in Constructive Approximation. Nashboro Press, Brentwood, Tennessee. ISBN 0-9728482-2-3

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Abstract

In this paper we study generalized interpolation problems as they typically arise in the context of collocation methods for numerically solving partial differential equations, as well as in the theory of fluid-structure interaction. We concentrate on fast evaluation methods based upon a far field expansion of the underlying kernel, which will be a Gaussian. Finally, we show how the fast evaluation method can ultimately be combined with a domain decomposition method. Interpolation by radial basis functions (RBFs) or, more generally, (conditionally) positive definite kernels has proven to be an efficient tool in the context of function and surface reconstruction. But the flexibility of the approach allows to extend applications of RBFs to much more general.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Holger Wendland
Date Deposited: 06 Feb 2012 20:57
Last Modified: 10 Jul 2012 12:09
URI: http://sro.sussex.ac.uk/id/eprint/28846
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