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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

Winter semester 2017/18

See teaching activities of the whole group.

Publications

  1. 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 Publisher arXiv
  2. 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 Publisher
  3. Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations. M. Griebel, C. Rieger, and P. Zaspel. Submitted to International Journal for Uncertainty Quantification. Also available as INS Preprint No. 1813, 2018. BibTeX PDF
  4. 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 Publisher arXiv
  5. Kernel-based reconstructions for parametric PDEs. R. Kempf, H. Wendland, and C. Rieger. Available as INS Preprint No. 1804., 2018. BibTeX PDF
  6. Incremental kernel based approximations for Bayesian inverse problems. C. Rieger. Available as INS Preprint No. 1807., 2018. BibTeX PDF
  7. Iterated Landweber method for radial basis functions interpolation with finite accuracy. C. Rieger. Submitted. Available as INS Preprint No. 1806., 2018. BibTeX PDF
  8. Sampling inequalities for anisotropic tensor product grids. C. Rieger and H. Wendland. Available as INS Preprint No. 1805., 2018. BibTeX PDF
  9. A representer theorem for deep kernel learning. B. Bohn, M. Griebel, and C. Rieger. Submitted to Journal of Machine Learning Research. Also available as INS Preprint No. 1714, 2017. BibTeX PDF
  10. 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 Publisher
  11. 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 Publisher
  12. Sampling inequalities for sparse grids. C. Rieger and H. Wendland. Numerische Mathematik, 2017. Also available as INS preprint no. 1609. BibTeX PDF Publisher
  13. Spectral Approximation in Reproducing Kernel Hilbert Spaces. C. Rieger. Habilitation, Institute for Numerical Simulation, University of Bonn, 2016. BibTeX
  14. 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 Publisher
  15. Improved exponential convergence rates by oversampling near the boundary. C. Rieger and B. Zwicknagl. Constructive Approximation, 39(2):323–341, 2014. BibTeX Publisher
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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. BibTeX
  21. Approximate interpolation with applications to selecting smoothing parameters. H. Wendland and C. Rieger. Numerische Mathematik, 101:729–748, 2005. BibTeX