Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes

TL;DR

This paper explores algebraic methods to characterize and construct dual univariate interpolating subdivision schemes through polynomial equations, establishing conditions for their existence.

Contribution

It introduces a constructive approach to find dual schemes using polynomial solutions and identifies conditions necessary for their existence.

Findings

Provided a method to construct dual schemes from polynomial equations

Identified conditions for the existence of dual univariate interpolating schemes

Enhanced understanding of algebraic properties of subdivision schemes

Abstract

The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of certain associated polynomial equations. The proposed approach also makes possible to identify conditions for the existence of the sought schemes.