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Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators
GE Fasshauer, Q Ye - Numerische Mathematik, 2011 - Springer
In this paper we introduce a generalized Sobolev space by defining a semi-inner product
formulated in terms of a vector distributional operator P consisting of finitely or countably …
formulated in terms of a vector distributional operator P consisting of finitely or countably …
Approximation of stochastic partial differential equations by a kernel-based collocation method
In this paper we present the theoretical framework needed to justify the use of a kernel-
based collocation method (meshfree approximation method) to estimate the solution of high …
based collocation method (meshfree approximation method) to estimate the solution of high …
Kernel bundle diffeomorphic image registration using stationary velocity fields and wendland basis functions
In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel
bundle framework for stationary velocity field-based image registration (Wendland kernel …
bundle framework for stationary velocity field-based image registration (Wendland kernel …
Green's functions: Taking another look at kernel approximation, radial basis functions, and splines
GE Fasshauer - Approximation Theory XIII: San Antonio 2010, 2011 - Springer
The theories for radial basis functions (RBFs) as well as piecewise polynomial splines have
reached a stage of relative maturity as is demonstrated by the recent publication of a number …
reached a stage of relative maturity as is demonstrated by the recent publication of a number …
Learning with boundary conditions
Kernel machines traditionally arise from an elegant formulation based on measuring the
smoothness of the admissible solutions by the norm in the reproducing kernel Hilbert space …
smoothness of the admissible solutions by the norm in the reproducing kernel Hilbert space …
Combining the boundary shift integral and tensor-based morphometry for brain atrophy estimation
M Michalkiewicz, A Pai, KK Leung… - Medical Imaging …, 2016 - spiedigitallibrary.org
Brain atrophy from structural magnetic resonance images (MRIs) is widely used as an
imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the …
imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the …