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 ℝ^d 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