学术报告与学术会议

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 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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