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

Alvise Sommariva; Marco Vianello

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arXiv · 2401.13322

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

Alvise Sommariva·Marco Vianello

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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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Alvise Sommariva, Marco Vianello. 2024-01-24. Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling. https://arxiv.org/abs/2401.13322

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