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

Publications of Priv.-Doz. Dr. Christian Rieger:

[1] D. Dũng, M. Griebel, V. N. Huy, and C. Rieger. ε-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs. Journal of Complexity, 46:66-89, 2018. Also available as INS Preprint No. 1703.
bib | DOI | arXiv | .pdf 1 ]
[2] M. Griebel, C. Rieger, and B. Zwicknagl. Regularized Kernel-Based Reconstruction in Generalized Besov Spaces. Foundations of Computational Mathematics, 18(2):459-508, 2018. Also available as INS Preprint No. 1517.
bib | DOI | .pdf 1 ]
[3] T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward. An inverse theorem for compact Lipschitz regions in Rd using localized kernel bases. Mathematics of Computation, 87:1949-1989, 2018.
bib | DOI | arXiv ]
[4] R. Kempf, H. Wendland, and C. Rieger. Kernel-based Reconstructions for Parametric PDEs. 2018. Available as INS Preprint No. 1804.
bib | .pdf 1 ]
[5] C. Rieger. Iterated Landweber Method for Radial Basis Functions Interpolation with Finite Accuracy. 2018. Available as INS Preprint No. 1806.
bib | .pdf 1 ]
[6] C. Rieger. Incremental Kernel Based Approximations for Bayesian Inverse Problems. 2018. Available as INS Preprint No. 1807.
bib | .pdf 1 ]
[7] C. Rieger and H. Wendland. Sampling Inequalities for Anisotropic Tensor Product Grids. 2018. Available as INS Preprint No. 1805.
bib | .pdf 1 ]
[8] 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.
bib | .pdf 1 ]
[9] 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.
bib | DOI | .pdf 1 ]
[10] 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.
bib | DOI | .pdf 1 ]
[11] C. Rieger and H. Wendland. Sampling inequalities for sparse grids. Numerische Mathematik, 2017. Also available as INS preprint no. 1609.
bib | DOI | .pdf 1 ]
[12] C. Rieger. Spectral Approximation in Reproducing Kernel Hilbert Spaces. Habilitation, Institute for Numerical Simulation, University of Bonn, 2016.
bib ]
[13] 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.
bib | DOI | .pdf 1 ]
[14] 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.
bib | arXiv ]
[15] C. Rieger and B. Zwicknagl. Improved exponential convergence rates by oversampling near the boundary. Constructive Approximation, 39(2):323-341, 2014.
bib | DOI ]
[16] 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.
bib ]
[17] 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.
bib ]
[18] 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.
bib ]
[19] 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.
bib ]
[20] H. Wendland and C. Rieger. Approximate interpolation with applications to selecting smoothing parameters. Numerische Mathematik, 101:729-748, 2005.
bib ]