Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling

2024/01/24 by Alvise Sommariva, Sommariva, Alvise, Marco Vianello +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2401.13322

openalex publication_date 2024/01/24 · openalex created_date 2024/01/26 · openalex updated_date 2026/07/28

Abstract

In a recent paper almost sure unisolvence of RBF interpolation at random points with no polynomial addition was proved, for Thin-Plate Splines and Radial Powers with noninteger exponent. The proving technique left unsolved the case of odd exponents. In this short note we prove almost sure polynomial-free unisolvence in such instances, by a deeper analysis of the interpolation matrix determinant and fundamental properties of analytic functions.

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