2025/07/15 by Hakop Hakopian, Hakopian, H., G. Vardanyan +3 · 1 citation
Computer Science · Engineering · Mathematics · #14H50 #41A05 #41A63 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2507.11207
openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28
Suppose X is an n-correct set of nodes in the plane, that is, it admits a unisolvent interpolation with bivariate polynomials of total degree less than or equal to n. Then an algebraic curve q of degree k≤ n can pass through at most d(n,k) nodes of \Xset, where d(n,k)=n+2\choose 2-n+2-k\choose 2. A curve q of degree k≤ n is called maximal if it passes through exactly d(n,k) nodes of X. In particular, a maximal line is a line passing through d(n,1)=n+1 nodes of X. Maximal curves are an important tool for the study of n-correct sets. We present new properties of maximal curves, as well as extensions of known properties.