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暨南大学 安聪沛副教授:A quick numerical trip to spherical t-designs

([西财资讯] 发布于 :2018-04-04 )

光华讲坛——社会名流与企业家论坛第4860

 

 A quick numerical trip to spherical t-designs

主讲人暨南大学 安聪沛副教授

主持人经济数学学院 孟开文

 2018年4月9日(星期一)15:00

 利记娱乐网柳林校区通博楼B412

主办单位:经济数学学院  科研处

 

主讲人概况:

安聪沛, 本科、硕士毕业于中南大学,师从向淑晃,博士毕业于香港理工大学,师从陈小君,Ian H. Sloan,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。主要研究兴趣包括球面布点与球面t-设计、球面最优化计算方法。主持国家自然科学基金二项,省部级自然基金一项,中央高校基金二项,在SIAM J. Numer. Anal.,J.Comput. and Appl. Math., Appl.Math and Comput. 等计算数学期刊发表论文多篇。多次应邀访问香港理工大学,香港中文大学,澳门大学,中国科学院数学与系统科学研究院等著名学术机构。

内容提要

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. Consequently, numerical approximation to singular integral over the sphere by using well conditioned spherical t-designs are also discussed.

 


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