Error Formulas for Ideal Interpolation

Abstract

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.