2026/03/31 by Toni Karvonen, Gabriele Santin, Tizian Wenzel
Computer Science · Mathematics · #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2603.01555
To appear in the proceedings of ENUMATH 2025
arxiv created 2026/08/03 · arxiv updated 2026/08/04
We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space W21(0, 1) is equipped with a suitable inner product, its reproducing kernel is piecewise linear and gives rise to piecewise linear interpolation. We show that such kernels are Green kernels for certain second-order partial differential equations and use kernel-based superconvergence theory to obtain rates of convergence for approximation of functions lying in W2s(0, 1) for s ∈ [1, 2]. The rates coincide with classical rates for linear splines.