Staff Priv.-Doz. Dr. Christian Rieger

On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data. M. Griebel, G. Li, and C. Rieger. Available as INS Preprint No. 2404, 2024. BibTeX PDF

On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data. M. Griebel, G. Li, and C. Rieger. Available as INS Preprint No. 2106, 2021. BibTeX PDF

A representer theorem for deep kernel learning. B. Bohn, M. Griebel, and C. Rieger. Journal of Machine Learning Research, 20(64):1–32, 2019. Also available as INS Preprint No. 1714. BibTeX PDF JMLR

Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations. M. Griebel, C. Rieger, and P. Zaspel. International Journal for Uncertainty Quantification, 9(5):471–492, 2019. Also available as INS Preprint No. 1813. BibTeX PDF DOI

Kernel-based reconstructions for parametric PDEs. R. Kempf, H. Wendland, and C. Rieger. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations IX, volume 129 of Lecture Notes in Computational Science and Engineering, 53–71. Springer, 2019. Also available as INS Preprint No. 1804. BibTeX PDF DOI

A particle method without remeshing. M. Kirchhart and C. Rieger. Preprint, 2019. BibTeX arXiv

Sampling inequalities for anisotropic tensor product grids. C. Rieger and H. Wendland. IMA Journal of Numerical Analysis, 2019. Online first. Also available as INS Preprint No. 1805. BibTeX PDF DOI

$\varepsilon$-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs. D. Dũng, M. Griebel, V. N. Huy, and C. Rieger. Journal of Complexity, 46:66–89, 2018. Also available as INS Preprint No. 1703. BibTeX PDF DOI arXiv

Regularized kernel-based reconstruction in generalized Besov spaces. M. Griebel, C. Rieger, and B. Zwicknagl. Foundations of Computational Mathematics, 18(2):459–508, 2018. Also available as INS Preprint No. 1517. BibTeX PDF DOI

An inverse theorem for compact Lipschitz regions in $R^d$ using localized kernel bases. T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. Mathematics of Computation, 87:1949–1989, 2018. BibTeX DOI arXiv

Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds, pages 517–543. T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. Springer International Publishing, Cham, 2018. BibTeX DOI

Incremental kernel based approximations for Bayesian inverse problems. C. Rieger. Available as INS Preprint No. 1807., 2018. BibTeX PDF

Iterated Landweber method for radial basis functions interpolation with finite accuracy. C. Rieger. Available as INS Preprint No. 1806., 2018. BibTeX PDF

Effects of a gamma DSD with variable shape parameter on polarimetric radar moments. K. Schinagl, C. Rieger, C. Simmer, S. Trömel, and P. Friederichs. 2018 19th International Radar Symposium (IRS), pages 1–10, 2018. BibTeX DOI

Reproducing kernel Hilbert spaces for parametric partial differential equations. M. Griebel and C. Rieger. SIAM/ASA J. Uncertainty Quantification, 5:111–137, 2017. also available as INS Preprint No. 1511. BibTeX PDF DOI

Upwind schemes for scalar advection-dominated problems in the discrete exterior calculus. M. Griebel, C. Rieger, and A. Schier. In D. Bothe and A. Reusken, editors, Transport Processes at Fluidic Interfaces, pages 145–175. Springer International Publishing, 2017. BibTeX PDF DOI

Sampling inequalities for sparse grids. C. Rieger and H. Wendland. Numerische Mathematik, 2017. Also available as INS preprint no. 1609. BibTeX PDF DOI

Spectral Approximation in Reproducing Kernel Hilbert Spaces. C. Rieger. Habilitation, Institute for Numerical Simulation, University of Bonn, 2016. BibTeX

Multiscale approximation and reproducing kernel Hilbert space methods. M. Griebel, C. Rieger, and B. Zwicknagl. SIAM Journal on Numerical Analysis, 53(2):852–873, 2015. Also available as INS Preprint No. 1312. BibTeX PDF DOI

Improved exponential convergence rates by oversampling near the boundary. C. Rieger and B. Zwicknagl. Constructive Approximation, 39(2):323–341, 2014. BibTeX DOI

An inverse theorem on bounded domains for meshless methods using localized bases. T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. ArXiv e-prints, 2014. Preprint. BibTeX arXiv

Sampling inequalities and support vector machines for Galerkin type data. C. Rieger. In Meshfree Methods for Partial Differential Equations V, volume 79 of Lecture Notes in Computational Science and Engineering, pages 51–63. Springer, New York, 2011. BibTeX DOI

Sampling and stability. C. Rieger, R. Schaback, and B. Zwicknagl. In Mathematical Methods for Curves and Surfaces, volume 5862 of Lecture Notes in Computer Science, pages 347–369. Springer, New York, 2010. BibTeX DOI

Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning. C. Rieger and B. Zwicknagl. Advances in Computational Mathematics, 32(1):103–129, 2010. BibTeX DOI

Deterministic error analysis of support vector regression and related regularized kernel methods. C. Rieger and B. Zwicknagl. Journal of Machine Learning Research, 10:2115–2132, 2009. PDF: http://jmlr.csail.mit.edu/papers/v10/rieger09a.html. BibTeX

Approximate interpolation with applications to selecting smoothing parameters. H. Wendland and C. Rieger. Numerische Mathematik, 101:729–748, 2005. BibTeX DOI