安聪沛教授受邀进行讲座

发布时间: 2017-11-29 23:28:00

题      目：A quick numerical trip to spherical t-designs

报 告 人：安聪沛教授 暨南大学

时      间：2017-11-29 10:30--11:30

地      点：学院401

报告人简介:

       安教授先后本科、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，暨南大学“双百英才”培养对象，广东省“千百十”校级培养对象，广东省计算数学会常务理事兼副秘书长。主要研究兴趣球面布点与球面t-设计。主持国家自然科学基金二项，省部级自然基金一项目，多次应邀访问国内外著名学术机构。

摘      要：

      We draw our attention on the unit sphere in three dimensional Euclidean space. A set 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 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 Riemannian manifolds. Consequently, numerical approximation to singular integral over the sphere by using well-conditioned spherical t-designs are also discussed.