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Open Access Green as soon as Postprint is submitted to ZB.
Error estimates for approximate operator inversion via Kernel-based methods.
Lect. Notes Comput. Sc. 9213, 399-413 (2015)
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,
Pages: 399-413
Publisher
Springer
Publishing Place
Berlin [u.a.]
Institute(s)
Institute of Computational Biology (ICB)