二元直交多项式的不变因子与数值积分公式

A．H．Stroud给出了关于二元m^2点2m-1次求积公式存在性的充分条件，即两个m次直交多项式P1(x，y)和p2(x，y)存在m^2个不同的公共零点，并且都不是无穷远点。本文用不变因子的方法给出了当m=2时这种直交多项式对的一种选取方法．另外，本文最后给出了一些2m-1次积分公式．     

一种新的二维区域上嵌入式数值积分公式构造方法

The purpose of this paper is to study a new strategy to construct embedded cubature formulae over two-dimensional regions.A new kind of embedded cubature formulae with some nodes along the selected algebraic curve is constructed.Some examples on the unit disk are presented to illustrate the validity of this strategy.     

一类多元全次数 Hermite 插值问题研究

In this paper we study a class of multivariate Hermite interpolation problem on 2~d nodes with dimension d ≥ 2 which can be seen as a generalization of two classical Hermite interpolation problems of d = 2. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved.