对称四方向双变量伪样条
Symmetric four-directional bivariate pseudo-splines
AI总结：
本文研究双变量伪样条的构造，提出一种对称四方向伪样条的符号公式，方法基于纯代数运算。
摘要：
单变量伪样条是均匀B-样条和插值2n点细分方案的推广。每种伪样条被定义为在特定多项式生成和再生度下具有最小支撑的细分方案。本文考虑双变量对应物的构造问题，并提供一族对称四方向双变量伪样条符号的公式。所用方法均为纯代数性质。
英文摘要：
Univariate pseudo-splines are a generalization of uniform B-splines and interpolatory $2n$-point subdivision schemes. Each pseudo-spline is characterized as the subdivision scheme with least possible support among all schemes with specific degrees of polynomial generation and reproduction. In this paper we consider the problem of constructing the symbols of the bivariate counterpart and provide a formula for the symbols of a family of symmetric four-directional bivariate pseudo-splines. All methods employed are of purely algebraic nature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
