2015/06/17 by Yihe Gong, Gong, Yihe, Xue Jiang +5
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Digital Filter Design and Implementation #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1506.05242
openalex publication_date 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the algebraic structure of error formulas for ideal interpolation. We introduce the so-called "normal" error formulas and prove that the lexicographic order reduced Gröbner basis admits such a formula for all ideal interpolation. This formula is a generalization of the "good" error formula proposed by Carl de Boor. Finally, we discuss a Shekhtman's example and give an explicit form of "normal" error formula for this example.