On thin plate spline interpolation

Abstract

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that $\mathcal{H}$-matrix techniques can successfully be employed to solve very large thin plate spline interpolation problems

Cited by in corpus (12)

• Nektar++: enhancing the capability and application of high-fidelity spectral/$hp$ element methods
• A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
• HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications
• Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
• Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system
• Hybrid multigrid methods for high-order discontinuous Galerkin discretizations
• Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations
• Multi-Physics Model Bias Correction with Data-Driven Reduced Order Modelling Techniques: Application to Nuclear Case Studies
• Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge--Kutta methods
• Scaling to the stars -- a linearly scaling elliptic solver for $p$-multigrid
• A hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity
• Model order reduction strategies for weakly dispersive waves