On existence of certain error formulas for a special class of ideal projectors

TL;DR

This paper proves the existence of 'good' error formulas for a special class of ideal projectors using algebraic geometry, and characterizes their minimal degree interpolation spaces.

Contribution

It establishes the existence of error formulas for a specific class of ideal projectors and analyzes their interpolation properties using algebraic geometry.

Findings

Existence of 'good' error formulas for the special class of ideal projectors.

Ranges of these projectors are minimal degree interpolation spaces.

Complete analysis of the interpolation conditions matched by these projectors.

Abstract

In this paper, we focus on a special class of ideal projectors. With the aid of algebraic geometry, we prove that for this special class of ideal projectors, there exist "good" error formulas as defined by C. de Boor. Furthermore, we completely analyze the properties of the interpolation conditions matched by this special class of ideal projectors, and show that the ranges of this special class of ideal projectors are the minimal degree interpolation spaces with regard to their associated interpolation conditions.