On a conjecture in bivariate interpolation

TL;DR

This paper provides a concise and straightforward proof of the Gasca-Maeztu conjecture for the case n=4 in bivariate interpolation, simplifying previous complex proofs.

Contribution

It offers a new, simplified proof of the Gasca-Maeztu conjecture for n=4, advancing understanding in bivariate polynomial interpolation.

Findings

Proof of the Gasca-Maeztu conjecture for n=4

Simplification of previous complex proofs

Enhanced understanding of bivariate interpolation

Abstract

The Gasca-Maeztu conjecture for the case $n=4$ was proved for the first time in [J. R. Busch, A note on Lagrange interpolation in $\mathbb{R}^2$, Rev. Un. Mat. Argentina, 36 (1990) 33--38]. Here we bring a short and simple proof of it.