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On the Gasca-Maeztu conjecture for \(n=6\)

A two-dimensional \(n\)-correct set is a set of nodes admitting unique bivariate interpolation with polynomials of total degree at most ~\(n\). We are interested in correct sets with the property that all fundamental polynomials are products of linear factors. In 1982, M.~Gasca and J.~I.~Maeztu conj...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Hakopian, Hakop, Vardanyan, Gagik, Vardanyan, Navasard
Format: Article
Language:English
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Summary:A two-dimensional \(n\)-correct set is a set of nodes admitting unique bivariate interpolation with polynomials of total degree at most ~\(n\). We are interested in correct sets with the property that all fundamental polynomials are products of linear factors. In 1982, M.~Gasca and J.~I.~Maeztu conjectured that any such set necessarily contains \(n+1\) collinear nodes. So far, this had only been confirmed for \(n\leq 5.\) In this paper, we make a step for proving the case \(n=6.\)
ISSN:2331-8422