报告人: 安聪沛副教授 （暨南大学）

报告题目: Well-conditioned spherical t-designs and its application in numerical integration

报告摘要：We draw our attention on the unit sphere in three dimensional Euclidean space. A set X_N of N points on the unit sphere is a spherical t-design if the average value of any polynomial of degree at most t over X_N is equal to the average value of the polynomial over the sphere. The last forty years have witnessed prosperous developments in theory and applications of spherical t-designs. Let integer t>0 be given. The most important question is how to construct a spherical t-design by minimal N. It is commonly conjectured that N=\frac{1}{2}t^2+o(t^2) point exists, but there is no proof. In this talk, we firstly review recent results on numerical construction of spherical t-designs by various of methods: nonlinear equations/interval analysis, variational characterization, nonlinear least squares, optimization on Riemanninan manifolds. Secondly, numerical construction of well-conditioned spherical t-designs are introduced for N is the dimension of the polynomial space. Consequently, numerical approximation to singular integral over the sphere by using well-conditioned spherical t-designs are also discussed.

报告人简介：安聪沛副教授本科、硕士毕业于中南大学，博士毕业于香港理工大学，现任暨南大学数学系副教授，硕士生导师，广东省计算数学会常务理事兼副秘书长。主要研究兴趣包括球面布点与球面t-设计、函数逼近等。主持国家自然科学基金二项，省部级自然基金一项，在SIAM Journal on Numerical Analysis等计算数学权威期刊发表论文多篇。

报告时间: 2017年12月18日（星期一）下午2:30-3:20

报告地点: 科技楼南楼702