2022/08/14 by Hakopian, Hakop, Vardanyan, Gagik, Vardanyan, Navasard
#14H50 #41A05 #41A63 #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2208.06784
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≤ 5. In this paper, we make a step for proving the case n=6.