In this paper we analyze a greedy procedure to approximate a linear functional defined in a reproducing kernel Hilbert space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals. For a large class of functionals, that includes integration functionals and other interesting cases, but does not include differentiation, we prove convergence results for the approximation by means of quasi-uniform and greedy points which generalize in various ways several known results. A perturbation analysis of the weights and node computation is also discussed. Beyond the theoretical investigations, we demonstrate numerically that our algorithm is effective in treating various integration densities, and that it is even very competitive when compared to existing methods for Uncertainty Quantification.
%0 Journal Article
%1 Santin2022
%A Santin, Gabriele
%A Karvonen, Toni
%A Haasdonk, Bernard
%D 2022
%J BIT Numerical Mathematics
%K liste EXC2075 ians fis imported unibibliografie haasdonk wenzel anm
%N 1
%P 279--310
%R 10.1007/s10543-021-00870-3
%T Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces
%U https://doi.org/10.1007/s10543-021-00870-3
%V 62
%X In this paper we analyze a greedy procedure to approximate a linear functional defined in a reproducing kernel Hilbert space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals. For a large class of functionals, that includes integration functionals and other interesting cases, but does not include differentiation, we prove convergence results for the approximation by means of quasi-uniform and greedy points which generalize in various ways several known results. A perturbation analysis of the weights and node computation is also discussed. Beyond the theoretical investigations, we demonstrate numerically that our algorithm is effective in treating various integration densities, and that it is even very competitive when compared to existing methods for Uncertainty Quantification.
@article{Santin2022,
abstract = {In this paper we analyze a greedy procedure to approximate a linear functional defined in a reproducing kernel Hilbert space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals. For a large class of functionals, that includes integration functionals and other interesting cases, but does not include differentiation, we prove convergence results for the approximation by means of quasi-uniform and greedy points which generalize in various ways several known results. A perturbation analysis of the weights and node computation is also discussed. Beyond the theoretical investigations, we demonstrate numerically that our algorithm is effective in treating various integration densities, and that it is even very competitive when compared to existing methods for Uncertainty Quantification.},
added-at = {2024-08-02T15:38:54.000+0200},
author = {Santin, Gabriele and Karvonen, Toni and Haasdonk, Bernard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/26dcc05761d8d643e0553ea2c63701b09/mathematik},
day = 01,
doi = {10.1007/s10543-021-00870-3},
interhash = {f9c6fb6625f52e133b91d8c3bfabf8f7},
intrahash = {6dcc05761d8d643e0553ea2c63701b09},
issn = {1572-9125},
journal = {BIT Numerical Mathematics},
keywords = {liste EXC2075 ians fis imported unibibliografie haasdonk wenzel anm},
month = mar,
number = 1,
pages = {279--310},
timestamp = {2024-08-02T15:38:54.000+0200},
title = {Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces},
url = {https://doi.org/10.1007/s10543-021-00870-3},
volume = 62,
year = 2022
}
