A note on polynomial-free unisolvence of polyharmonic splines at random points

TL;DR

This paper proves that polyharmonic splines can interpolate data at random points with high probability without needing polynomial terms, simplifying the understanding of their unisolvence properties.

Contribution

It establishes almost sure unisolvence of RBF interpolation using a broad class of polyharmonic splines without polynomial augmentation.

Findings

Almost sure unisolvence of RBF interpolation at random points.

Polyharmonic splines, including Thin-Plate Splines, do not require polynomial addition for unisolvence.

Simplifies the theoretical understanding of RBF interpolation at random points.

Abstract

In this note we prove almost sure unisolvence of RBF interpolation on randomly distributed sequences by a wide class of polyharmonic splines (including Thin-Plate Splines), without polynomial addition.