报告题目：Approximation based on orthogonal polynomials and their roots

报 告 人：向淑晃教授（中南大学）

报告时间：2021年3月17日  10:30-11:30

报告地点：数统院5楼数学研究中心多功能研讨室

报告摘要：

Based on the Hilb typc formula betwccn Jacobi polynomials and Bcssel functions, optimal decayratcs on Jacobi cxpansiom coefficients are derived, by applying van der Corput typc lemmas,forfuncetions of algebraic and logarithmatic singularities, which leads tothe optimal convergence rates on theJacobi,Gcgenbaucr and Chebyshev orthogonal projections,It is intecresting to see that for boundarysingularitics,onc may get fastcr convergcncec ratc on the Jacobi or Gicgenbaucr projection asS(Calpha, beta)S and SMambdaS increascs. The larger values of parametcr,the higher convergence ratescan be achieved. ln particular,the Legendre projcction has one half order higher than Chebyshev.Morcover，ifSimin\A lalpha, beta. >0S and Slambda>'frac{1}{2}S, the Jacobi and Gicgcnbauerorthogonal projections have higher convergence orders compared with Legendre.While for intcriorsingularity, the convergence order is independent of S(alpha, ,bcta )$ and SIambdla$.

Furthermore,rational baryccnteric interpolation based on the roots of orthogonal polynomials areintroduccd to fast approximation of functions and thcir dcrivatives of singu laritics.

报告人简介：

向淑晃，中南大学二级教授、博士生导师，2006年入选教育部新世纪优秀人才计划，2011年入选湖南省学科带头人培养计划，2019年4月至今担任湖南省计算数学与应用软件学会理事长。主要从事正交多项式逼近的快速、高精度算法以及高频振荡问题高效计算与收敛性研究。有Wang-Xiang提出的重心权公式，为国际上高震荡问题计算研究的领先团队之一，在SIAMJ. Nurner.Anal, SIAM J.Sci. Comput., SIAM J.Optimization, Math.Program., Numer. Math., Math. Comput.等刊物发表论文100余篇。研究成果得到了美国工程院院士、英国皇家院士、欧洲科学院院士、德国科学院院士、印度两院院士等国际权战专家的广泛引用和高度评价。