Publications
- 2021:1
-
Discrete Projections: A Step Towards Particle Methods on Bounded Domains without Remeshing
M. Kirchhart and C. Rieger
SIAM Journal on Scientific Computing
43(1)
A609--A635
(2021)
https://doi.org/10.1137/19M1299864
- 2020:1
-
Sampling Inequalities for Anisotropic Tensor Product Grids
C. Rieger and H. Wendland
IMA Journal of Numerical Analysis
40
285--321
(2020)
https://doi.org/10.1093/imanum/dry080
- 2019:3
-
A Representer Theorem for Deep Kernel Learning
B. Bohn and M. Griebel and C. Rieger
Journal of Machine Learning Research
20
1-32
(2019)
http://jmlr.org/papers/v20/17-621.html
- 2019:2
-
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
M. Griebel and C. Rieger and P. Zaspel
International Journal for Uncertainty Quantification
9
471--492
(2019)
http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2019029228
- 2019:1
-
Kernel-based Reconstructions for Parametric PDEs
R. Kempf and H. Wendland and C. Rieger
Meshfree Methods for Partial Differential Equations IX
Editors: M. Griebel and M. A. Schweitzer
Lecture Notes in Computer Science
129
53--71
(2019)
Springer International Publishing
http://dx.doi.org/10.1007/978-3-030-15119-5
- 2018:4
-
ϵ-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs
D. Dung and M. Griebel and V. N. Huy and C. Rieger
Journal of Complexity
46
66--89
(2018)
http://dx.doi.org/10.1016/j.jco.2017.12.001
- 2018:3
-
Regularized Kernel-Based Reconstruction in Generalized Besov Spaces
M. Griebel and C. Rieger and B. Zwicknagl
Foundations of Computational Mathematics
18
459--508
(2018)
http://dx.doi.org/10.1007/s10208-017-9346-z
- 2018:2
-
An inverse theorem for compact Lipschitz regions in ℝd using localized kernel bases
T. Hangelbroek and F. J. Narcowich and C. Rieger and J. D. Ward
Mathematics of Computation
87
1949--1989
(2018)
http://dx.doi.org/10.1090/mcom/3256
- 2018:1
-
Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
T. Hangelbroek and F. J. Narcowich and C. Rieger and J. D. Ward
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
517--543
(2018)
Editors: J. Dick and F.J. Kuo and H. Woźniakowski
Springer International Publishing
http://dx.doi.org/10.1007/978-3-319-72456-0_24
- 2017:3
-
Reproducing kernel Hilbert spaces for parametric partial differential equations
M. Griebel and C. Rieger
SIAM/ASA J. Uncertainty Quantification
5
111-137
(2017)
http://dx.doi.org/10.1137/15M1026870
- 2017:2
-
Upwind Schemes for Scalar Advection-Dominated Problems in the Discrete Exterior Calculus
M. Griebel and C. Rieger and A. Schier
Transport Processes at Fluidic Interfaces
Editors: D. Bothe and A. Reusken
Advances in Mathematical Fluid Mechanics
145--175
(2017)
Springer International Publishing
http://dx.doi.org/10.1007/978-3-319-56602-3_6
- 2017:1
-
Sampling Inequalities for Sparse Grids
C. Rieger and H. Wendland
Numerische Mathematik
(2017)
http://dx.doi.org/10.1007/s00211-016-0845-7
- 2015:1
-
Multiscale approximation and reproducing kernel Hilbert space methods
M. Griebel and C. Rieger and B. Zwicknagl
SIAM Journal on Numerical Analysis
53
852-873
(2015)
http://dx.doi.org/10.1137/130932144
- 2014:1
-
Improved Exponential Convergence Rates by Oversampling Near the Boundary
C. Rieger and B. Zwicknagl
Constructive Approximation
39(2)
323-341
(2014)
http://dx.doi.org/10.1007/s00365-013-9211-5
- 2011:1
-
Sampling Inequalities and Support Vector Machines for Galerkin Type Data
C. Rieger
Meshfree Methods for Partial Differential Equations V
Editors: M. Griebel and M. A. Schweitzer
Lecture Notes in Computer Science
79
51-63
(2011)
Springer International Publishing
http://dx.doi.org/10.1007/978-3-642-16229-9_3
- 2010:2
-
Sampling and Stability
C. Rieger and R. Schaback and B. Zwicknagl
Mathematical Methods for Curves and Surfaces
Editors: M. Dæhlen and M. Floater and T. Lyche and J.-L. Merrien and K. Mørken and L. L. Schumaker
Lecture Notes in Computer Science
5862
347-369
(2010)
http://dx.doi.org/10.1007/978-3-642-11620-9_23
- 2010:2
-
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)
http://dx.doi.org/10.1007/s10444-008-9089-0
- 2009:1
-
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)
http://jmlr.csail.mit.edu/papers/v10/rieger09a.html
- 2005:1
-
Approximate Interpolation with Applications to Selecting Smoothing Parameters
H. Wendland and C. Rieger
Numerische Mathematik
101
729-748
(2005)
http://dx.doi.org/10.1007/s00211-005-0637-y
Other Publications and Preprints
- 2021:1
-
On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete datas
M. Griebel and G. Li and C. Rieger
INS Preprint 2106
(2018)
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint2106.pdf?pk=1587
- 2018:1
-
Incremental Kernel Based Approximations for Bayesian Inverse Problems
C. Rieger
INS Preprint 1807
(2018)
http://wissrech.ins.uni-bonn.de/research/pub/rieger/INSPreprint1807.pdf
- 2018:2
-
Iterated Landweber Method for Radial Basis Functions Interpolation with Finite Accuracy
C. Rieger
INS Preprint 1806
(2018)
http://wissrech.ins.uni-bonn.de/research/pub/rieger/INSPreprint1806.pdf
- 2018:3
-
Effects of a gamma DSD with variable shape parameter on polarimetric radar moments
K. Schinagl and C. Rieger and C. Simmer and S. Trömel and P. Friederichs
2018 19th International Radar Symposium (IRS)
1-10
(2018)
http://dx.doi.org/10.23919/IRS.2018.8448252