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发表时间:2021-01-15 阅读次数:396次
报告题目: A quick numerical trip to spherical t-designs
报 告 人:安聪沛 教授
报告人所在单位:西南财经大学经济数学学院
报告日期:2021-01-15 星期五
报告时间:10:00-11:00
报告地点:腾讯会议ID: 187364013, 密码: 200433
  
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.

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