Regularized kernel based reconstruction in generalized Besov spaces
Regularized kernel based reconstruction in generalized Besov spaces
dc.contributor.author | Griebel, Michael | |
dc.contributor.author | Rieger, Christian | |
dc.contributor.author | Zwicknagl, Barbara | |
dc.date.accessioned | 2024-08-21T09:24:18Z | |
dc.date.available | 2024-08-21T09:24:18Z | |
dc.date.issued | 2015 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/11898 | |
dc.description.abstract | We present a theoretical framework for reproducing kernel based reconstruction methods in certain generalized Besov spaces based on positive, essentially self-adjoint operators. An explicit representation of the reproducing kernel is given in terms of an infinite series. We provide stability estimates for the kernel, including inverse Bernstein-type estimates for kernel-based trial spaces, and we give condition estimates for the interpolation matrix. Then, a deterministic error analysis for regularized reconstruction schemes is presented by means of sampling inequalities. In particular, we provide error bounds for a regularized reconstruction scheme based on a numerically feasible approximation of the kernel. This allows us to derive explicit coupling relations between the series truncation, the regularization parameters and the data set. | en |
dc.format.extent | 41 | |
dc.language.iso | eng | |
dc.relation.ispartofseries | INS Preprints ; 1517 | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Reproducing kernels | |
dc.subject | A priori error analysis | |
dc.subject | Generalized Besov spaces | |
dc.subject | Feasible reconstruction schemes | |
dc.subject | Spline smoothing | |
dc.subject.ddc | 510 Mathematik | |
dc.subject.ddc | 518 Numerische Analysis | |
dc.title | Regularized kernel based reconstruction in generalized Besov spaces | |
dc.type | Preprint | |
dc.publisher.name | Institut für Numerische Simulation (INS) | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.relation.doi | https://doi.org/10.1007/s10208-017-9346-z | |
ulbbn.pubtype | Zweitveröffentlichung | |
dcterms.bibliographicCitation.url | https://ins.uni-bonn.de/publication/preprints |
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