关键词： 三角域, 二元三次插值, Bezout定理

Abstract: Some interpolation on two dimensional Euler space of triangular domain is studied.The authors advance three kinds of problems about polynomial interpolation of cubic polynomial with two unknown,and prove the existence,the uniqueness with Bezout's theorem and the feasibility of solving polynomial interpolation of cubic polynomial with two unknown on triangular domain by example.

Key words: triangular domain;polynomial interpolation of cubic polynomial with two unknown;Bezout's , theorem