报告人：向淑晃教授

报告题目：Fast and stable barycentric rational interpolation for (near) singular functions

报告摘要：

(1) We will present fast and stable rational interpolation to approximate (near) singular functions. Based upon the logarithmic equilibrium potential, a barycentric interpolation algorithm with specific exponential convergence is developed for analytic functions defined on the complex plane with singularities in the vicinity of the interpolation region, where the region is compact and could be disconnected or multiconnected. Furthermore, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin.

(2) To avoid singularity, the technique of singularity separation is applied and then the singular ODE occurring in classic Levin methods is converted into two kinds of non-singular ODEs. The solutions of one can be obtained explicitly, while those of the other can be solved efficiently by collocation methods. The proposed methods can attach arbitrarily high asymptotic orders and also enjoy superalgebraic convergence with respect to the number of collocation points.

报告时间：2022年6月18日08:00-11:00

报告形式：腾讯会议；会议号：509-560-290

报告人简介：向淑晃，中南大学教授、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，2004年11月-2005 年9月年获日本JSPS振兴会特邀长期研究员资助任弘前大学研究员，2003年9 月-2004年9月访问剑桥大学，2007年2-3月应邀访问世界数学中心之一剑桥大学牛顿数学所，2008年9月-2009年9月香港理工大学研究员，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的渐进理论、高效计算与收敛性研究，在SIAM J. Numer. Anal.、SIAM J. Sci. Comp.、SIAM J. Optimization、Math. Program.、Numer. Math.、Math. Comp.等期刊发表论文100余篇，2021年获教育部自然科学二等奖。