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Error estimates for approximate operator inversion via Kernel-based methods.

Lect. Notes Comput. Sc. 9213, 399-413 (2015)
Open Access Green as soon as Postprint is submitted to ZB.
In this paper we investigate error estimates for the approximate solution of operator equations Af = u, where u needs not to be a function on the same domain as f. We use the well-established theory of generalized interpolation, also known as optimal recovery in reproducing kernel Hilbert spaces, to generate an approximation to f from finitely many samples u(x1),…, u(xN). To derive error estimates for this approximation process we will show sampling inequalities on fairly general Riemannian manifolds.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Generalized Interpolation ; Positive Definite Functions ; Reproducing Kernel Hilbert Spaces ; Sampling Inequalities On Manifolds
ISSN (print) / ISBN 0302-9743
e-ISSN 1611-3349
Conference Title 8th International Conference on Curves and Surfaces
Conference Date 12-18 June 2014
Conference Location Paris, France
Quellenangaben Volume: 9213, Issue: , Pages: 399-413 Article Number: , Supplement: ,
Publisher Springer
Publishing Place Berlin [u.a.]