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学术报告四十六:Well conditioned spherical t-designs and its application in numerical integration

来源:数学与统计学院     作者:     时间:2018/6/11 16:19:40  0次

数学与统计学院学术报告[2018] 046

(高水平大学建设系列报告165)

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

报告人:安聪沛   副教授  (暨南大学

报告时间:20186121530-1630

报告地点: 科技楼501

报告邀请人:胡耀华                  

报告内容:We draw our attention on the unit sphere in three dimensional Euclidean space. The last forty years have witnessed prosperous developments in theory and applications of spherical t-designs. 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.

报告人简历:安聪沛,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。

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