Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

Priv.-Doz. Dr. Christian Rieger

Address: Institut für Numerische Simulation
Wegelerstr. 6
53115 Bonn
Office: We4 0.012
Phone: +49 228 7360462


Theses (co-supervised)

[1] A. Schier. Discrete Exterior Calculus im maschinellem Lernen. Diplomarbeit, Institut für Numerische Simulation, Universität Bonn, 2014.
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[1] B. Bohn, M. Griebel, and C. Rieger. A representer theorem for deep kernel learning. 2017. Submitted to Journal of Machine Learning Research. Also available as INS Preprint No. 1714.
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[2] D. Dũng, M. Griebel, V. N. Huy, and C. Rieger. ε-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs. 2017. Accepted by Journal of Complexity, also available as INS Preprint No. 1703.
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[3] M. Griebel and C. Rieger. Reproducing kernel Hilbert spaces for parametric partial differential equations. SIAM/ASA J. Uncertainty Quantification, 5:111-137, 2017. also available as INS Preprint No. 1511.
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[4] M. Griebel, C. Rieger, and A. Schier. Upwind schemes for scalar advection-dominated problems in the discrete exterior calculus. In D. Bothe and A. Reusken, editors, Transport Processes at Fluidic Interfaces, pages 145-175. Springer International Publishing, 2017. also available as INS Preprint No. 1627.
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[5] C. Rieger and H. Wendland. Sampling inequalities for sparse grids. Numerische Mathematik, 2017. Also available as INS preprint no. 1609.
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[6] C. Rieger. Spectral Approximation in Reproducing Kernel Hilbert Spaces. Habilitation, Institute for Numerical Simulation, University of Bonn, 2016.
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[7] M. Griebel, C. Rieger, and B. Zwicknagl. Multiscale approximation and reproducing kernel Hilbert space methods. SIAM Journal on Numerical Analysis, 53(2):852-873, 2015. Also available as INS Preprint No. 1312.
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[8] M. Griebel, C. Rieger, and B. Zwicknagl. Regularized kernel based reconstruction in generalized Besov spaces. 2015. Accepted for publication in Foundations of Computational Mathematics. Also available as INS Preprint No. 1517.
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[9] T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. An inverse theorem for compact Lipschitz regions in Rd using localized kernel bases. 2015. accepted for publication in "Mathematics of Computation".
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[10] T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. An inverse theorem on bounded domains for meshless methods using localized bases. ArXiv e-prints, 2014. Preprint.
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[11] C. Rieger and B. Zwicknagl. Improved exponential convergence rates by oversampling near the boundary. Constructive Approximation, 39(2):323-341, 2014.
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[12] C. Rieger. Sampling inequalities and support vector machines for Galerkin type data. 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.
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[13] C. Rieger, R. Schaback, and B. Zwicknagl. Sampling and stability. In Mathematical Methods for Curves and Surfaces, volume 5862 of Lecture Notes in Computer Science, pages 347-369. Springer, New York, 2010.
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[14] C. Rieger and B. Zwicknagl. Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning. Advances in Computational Mathematics, 32(1):103-129, 2010.
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[15] C. Rieger and B. Zwicknagl. Deterministic error analysis of support vector regression and related regularized kernel methods. Journal of Machine Learning Research, 10:2115-2132, 2009.
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[16] H. Wendland and C. Rieger. Approximate interpolation with applications to selecting smoothing parameters. Numerische Mathematik, 101:729-748, 2005.
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