**数学与系统科学研究院**

**计算数学所学术报告会**

**报告人：**
Prof. Zhiqiang Xu

**报告题目：**

Using Multivariate Splines to Study Problems in Discrete Mathematics

**报告摘要：**

It is well known that multivariate splines are an important tool in numerical ana
lysis. In this talk, we shall show multivariate splines are also very useful for
solving problems in discrete mathematics. We shall survey some results as follow
s about solving problems in discrete mathematics using multivariate splines.

1. By using multivariate splines, we shall give an explicit formulation for coun
ting non-negative solutions for linear Diophantine equations.

2. We shall show the iterated formulation for computing multivariate cone spline
s can be used to compute the volume of convex polytopes. Hence, some famous formu
lations about volume computation of polytopes follow from the properties of multi
variate cone splines.

3. According to multivariate Box splines, the famous Popoviciu's formulation in
number theory is generalized.

4. An explicit formulation for Ehrhart polynomial which counts integer points in
polytopes is also given.

Finally, some challenging problems in this area are also raised.

**报告时间：**
2006年5月11日(周四) 下午4:00--5:00

**报告地点：**科技综合楼三层311报告厅

欢迎大家参加!