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Piecewise Linear Interpolation via Kernels

MCML Authors

Tizian Wenzel

Dr.

→ Group Holger Rauhut
Mathematical Data Science and Artificial Intelligence

Abstract

We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space W12(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 Ws2(0,1) for s∈[1,2]. The rates coincide with classical rates for linear splines.

misc KSW+26