On iterated interpolation

TL;DR

This paper introduces a novel, elegant method for analyzing errors in multi-level iterated interpolation of kernel matrices, enhancing efficiency and extending to derivatives of the kernel function.

Contribution

It provides a new analytical framework for error estimation in iterated interpolation, applicable to kernels and their derivatives, improving upon previous methods.

Findings

New error analysis approach for iterated interpolation

Applicable to kernel functions and derivatives

Enhances efficiency of matrix approximations

Abstract

Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a multi-level approach can be employed that involves interpolating the kernel function and its approximations multiple times. This article presents a new approach to analyze the error incurred by these iterated interpolation procedures that is considerably more elegant than its predecessors and allows us to treat not only the kernel function itself, but also its derivatives.