报告地点：行健楼学术活动室665
邀请人：孙海琳教授
摘要：We discuss the approximation of continuous functions on the unit sphere by spherical polynomials of degree n via hyperinterpolation. Hyperinterpolation of degree n is a discrete approximation of the L2-orthogonal projection of degree n with its Fourier coefficients evaluated by a positive-weight quadrature rule that exactly integrates all spherical polynomials of degree at most 2n. This talk aims to bypass this quadrature exactness assumption by replacing it with the Marcinkiewicz--Zygmund property. Consequently, hyperinterpolation can be constructed by a positive-weight quadrature rule--not necessarily with quadrature exactness. This scheme is called unfettered hyperinterpolation. We provide a reasonable error estimate for unfettered hyperinterpolation. The error estimate generally consists of two terms: a term representing the error estimate of the original hyperinterpolation of full quadrature exactness and another introduced as compensation for the loss of exactness degrees. A guide to controlling the newly introduced term in practice is provided. In particular, if the quadrature points form a quasi-Monte Carlo design, then there is a refined error estimate. Numerical experiments verify the error estimates and the practical guide.
报告人简介：安聪沛, 本科、硕士毕业于中南大学，博士毕业于香港理工大学，现为西南财经大学数学学院副教授、博导。入选四川省"天府峨眉计划",最近又获得2023年四川省数学会应用数学一等奖。美国《数学评论》评论员，主持过三项国家自然科学基金。 在构造逼近，球面t设计，反问题计算等领域取得了国际同行关注的结果，例如2022年菲尔兹奖得主Maryna Viasovska就证明过安聪沛与和作者提出的关于球t-设计猜想。
