5 papers · 1 filter
Reliable sampling-based RKHS norm estimation via superconvergence
Tizian Wenzel, Abdullah Tokmak, Christian Fiedler
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learni…
Piecewise linear interpolation via kernels
Toni Karvonen, Gabriele Santin, Tizian Wenzel
We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space is equipped with a suitable inner product…
Sharp inverse statements for kernel approximation: Superconvergence and saturation
Tizian Wenzel
This article establishes sharp inverse and saturation statements for kernel-based approximation using finitely smooth Sobolev kernels on bounded Lipschitz regions. The analysis foc…
Sobolev Algorithm for Local Smoothness Analysis (SALSA) via Sharp Direct and Inverse Statements
Sara Avesani, Leevan Ling, Francesco Marchetti +1
We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spac…
Spectral alignment of kernel matrices and applications
Tizan Wenzel, Armin Iske
Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this wo…