On the convergence of generalized kernel-based interpolation by greedy data selection algorithms

TL;DR

This paper studies the convergence properties of generalized kernel-based interpolation methods, demonstrating that popular greedy data selection algorithms converge under minimal assumptions, with numerical results in tomography supporting the theory.

Contribution

It provides a convergence analysis of kernel-based interpolation with greedy algorithms under minimal assumptions, extending understanding of their theoretical guarantees.

Findings

Greedy algorithms converge for totally bounded sets of sampling functionals.

Convergence holds under minimal assumptions on kernels and target functions.

Numerical results in tomography illustrate the theoretical findings.

Abstract

We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data selection algorithms for totally bounded sets of sampling functionals. Supporting numerical results concerning computerized tomography are provided for illustration.