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  • Constructing least-squares multivariate polynomial approximation

    发布者:文明办发布时间:2019-11-18浏览次数:52


    主讲人:周涛 中国科学院数学与系统科学研究院副研究员


    时间:2019年11月22日11:15


    地点:3号楼322报告厅


    举办单位:数理学院


    主讲人介绍:周涛,中国科学院数学与系统科学研究院副研究员。曾于瑞士洛联邦理工大学从事博士后研究。主要研究方向为不确定性量化、随机计算方法以及高维逼近算法等。2016年获中国工业与应用数学学会青年科技奖,2017年获中科院数学与系统科学研究院“陈景润未来之星”称号,并获中科院数学与系统科学研究院“2017年十大科研进展”,2018年获国家自然科学基金委“优秀青年科学基金”资助。  2017年起担任国际不确定性量化期刊(International Journal for UQ)副总编(Associate Editor in  Chief)。同时担任Commun. Comput. Phys. 和Numerical Mathematics: TMA  两国际期刊编委,2018年起任国际期刊East Asian J. Appl. Math.执行主编(Managing Editor)。2019年受邀担任SIAM  J Sci Comput编委。国防科工委科学挑战专题领域一“复杂系统模型不确定性评定方法”首席科学家。


    内容介绍:Polynomial approximations constructed using a least squares approach is a  ubiquitous technique in numerical computations. One of the simplest ways to  generate data for the least squares problems is with random sampling of a  function. We discuss theory and algorithms for stability of the least-squares  problem using random samples. The main lesson from our discussion is that the  intuitively straightforward (``standard) density for sampling frequently yields  suboptimal approximations, whereas sampling from a non-standard density either  by the so-called induced distribution or the asymptotic equilibrium measure,  yields near-optimal approximations. We present recent theory that demonstrates  why sampling from such measures is optimal, and provide several computational  experiments that support the theory. New applications of the equilibrium measure  sampling will also be discussed.