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Papers - Christian Rieger

• T. Hangelbroek, C. Rieger, Kernel Multi-Grid on Manifolds, J. Complexity, Special Issue on Parabolic PDEs, 2024
• T. Hangelbroek and C. Rieger, Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms, Math. Comp, 2024.
• C. Rieger and H. Wendland, On the approximability and curse of dimensionality of certain classes of high-dimensional functions, SIAM J. Numer. Anal.,  62 (2024)
• W. Erb,  T. Hangelbroek,  F. J. Narcowich, C. Rieger,  J. D. Ward,  Highly localized RBF Lagrange functions for finite difference methods on spheres, BIT Numerical Mathematics , 64 (2024)
• M. Kirchhart and C. Rieger, Discrete projections: a step towards particle methods on bounded domains without remeshing, SIAM J. Sci. Comput. 43 (2021)
• C. Rieger and H. Wendland, Sampling inequalities for anisotropic tensor product grids, IMA J. Numer. Anal.  40 (2020)
• R. Kempf, H. Wendland and C. Rieger, Kernel-based reconstructions for parametric PDEs, in Meshfree methods for partial differential equations IX, 53--71, Lect. Notes Comput. Sci. Eng., 129, Springer, Cham
• M. Griebel, C. Rieger and P. Zaspel, Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations, Int. J. Uncertain. Quantif. 9 (2019
• B. Bohn, C. Rieger and M. Griebel, A representer theorem for deep kernel learning, J. Mach. Learn. Res.  20 (2019)
• T. Hangelbroek,  F. J. Narcowich, C. Rieger,  J. D. Ward, Direct and inverse results on bounded domains for meshless methods via localized bases on manifolds, in Contemporary computational mathematics---a celebration of the 80th birthday of Ian Sloan. Vol. 1, 2, 517--543, Springer, Cham
• T. Hangelbroek,  F. J. Narcowich, C. Rieger,  J. D. Ward, An inverse theorem for compact Lipschitz regions in R^d using localized kernel bases, Math. Comp.  87 (2018)
• M. Griebel, C. Rieger and B. Zwicknagl, Regularized kernel-based reconstruction in generalized Besov spaces, Found. Comput. Math.  18 (2018)
• D.Dung, M. Griebel, V. N. Huy, C. Rieger , ε-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs, J. Complexity  46 (2018)
• M. Griebel, C. Rieger and A. Schier, Upwind schemes for scalar advection-dominated problems in the discrete exterior calculus, in Transport processes at fluidic interfaces, 145--175, Adv. Math. Fluid Mech., Birkhäuser/Springer, Cham
• C. Rieger and H. Wendland, Sampling inequalities for sparse grids, Numer. Math. 136 (2017)
• M. Griebel and C. Rieger, Reproducing kernel Hilbert spaces for parametric partial differential equations, SIAM/ASA J. Uncertain. Quantif. 5 (2017)
• M. Griebel, C. Rieger and B. Zwicknagl, Multiscale approximation and reproducing kernel Hilbert space methods, SIAM J. Numer. Anal. 53 (2015)
• C. Rieger and B. Zwicknagl, Improved exponential convergence rates by oversampling near the boundary, Constr. Approx. 39 (2014)
• C. Rieger, Sampling inequalities and support vector machines for Galerkin type data, in  Meshfree methods for partial differential equations V, 51--63, Lect. Notes Comput. Sci. Eng., 79, Springer, Heidelberg
• C. Rieger, R. Schaback and B. Zwicknagl, Sampling and stability, in  Mathematical methods for curves and surfaces, 347--369, Lecture Notes in Comput. Sci., 5862, Springer, Berlin
• C. Rieger and B. Zwicknagl, Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning, Adv. Comput. Math.  32 (2010)
• C. Rieger and B. Zwicknagl, Deterministic error analysis of support vector regression and related regularized kernel methods, J. Mach. Learn. Res.  10 (2009)
• H. Wendland and C. Rieger, Approximate interpolation with applications to selecting smoothing parameters, Numer. Math. 101 (2005)