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Staff Priv.-Doz. Dr. Christian Rieger

Contact Information

Address:
Institut für Numerische Simulation
Endenicher Allee 19b
53115 Bonn
Phone: +49 228 73-69813
Office: EA19b 3.005
E-Mail: ed tod nnob-inu tod sni ta regeira tod b@foo tod de

beurlaubt für das WS18/19, Aachen:
http://www.mathcces.rwth-aachen.de/5people/rieger/start

Teaching

Summer semester 2019

  • Mathematik Vorkurs BA Block seminar.

See teaching activities of the whole group.

Publications

  1. 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
  2. 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
  3. ε\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 arXiv
  4. 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
  5. Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations. M. Griebel, C. Rieger, and P. Zaspel. Accepted by International Journal for Uncertainty Quantification. Also available as INS Preprint No. 1813, 2018. BibTeX PDF
  6. An inverse theorem for compact Lipschitz regions in RdR^d using localized kernel bases. T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. Mathematics of Computation, 87:1949–1989, 2018. BibTeX arXiv
  7. 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
  8. Kernel-based reconstructions for parametric PDEs. R. Kempf, H. Wendland, and C. Rieger. Accepted for publication in: Meshfree Methods for Partial Differential Equations IX, Springer, Lecture Notes in Computational Science, editors: M. Griebel and M. A. Schweitzer. Also available as INS Preprint No. 1804., 2018. BibTeX PDF
  9. Incremental kernel based approximations for Bayesian inverse problems. C. Rieger. Available as INS Preprint No. 1807., 2018. BibTeX PDF
  10. Iterated Landweber method for radial basis functions interpolation with finite accuracy. C. Rieger. Available as INS Preprint No. 1806., 2018. BibTeX PDF
  11. 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
  12. 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
  13. 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
  14. Sampling inequalities for sparse grids. C. Rieger and H. Wendland. Numerische Mathematik, 2017. Also available as INS preprint no. 1609. BibTeX PDF
  15. Spectral Approximation in Reproducing Kernel Hilbert Spaces. C. Rieger. Habilitation, Institute for Numerical Simulation, University of Bonn, 2016. BibTeX
  16. 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
  17. Improved exponential convergence rates by oversampling near the boundary. C. Rieger and B. Zwicknagl. Constructive Approximation, 39(2):323–341, 2014. BibTeX
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. Approximate interpolation with applications to selecting smoothing parameters. H. Wendland and C. Rieger. Numerische Mathematik, 101:729–748, 2005. BibTeX