关于举行西南财经大学安聪沛副教授学术报告会的通知

报告题目: Regularized weighted least squares approximation by orthogonal polynomials

报  告  人: 安聪沛  副教授(西南财经大学)

报告时间: 2019年7 月8 日（星期四上午）10:30-11:30             

报告地点：4号楼318 室

邀  请  人: 潘少华  教授

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数学学院

2019年7月3日

报告摘要：

We consider polynomial approximation over the interval [-1,1] by a class of regularized weighted discrete least squares methods with $\ell_2$-regularization and $\ell_1$-regularization terms, respectively. It is merited to choose classical orthogonal polynomials as basis sets of polynomial space with degree at most $L$. As node sets we use zeros of orthogonal polynomials such as Chebyshev points of the first kind, Legendre points. The number of nodes, say $N+1$, is chosen to ensure $L\leq2N+1$. With the aid of Gauss quadrature, we obtain approximation polynomials of degree $L$ in closed form without solving linear algebra or optimization problem. As a matter of fact, these approximation polynomials can be expressed in the form of barycentric interpolation formula when the interpolation condition is satisfied. We then study the approximation quality of $\ell_2$-regularization approximation polynomial, especially on the Lebesgue constant. Moreover, the sparsity of $\ell_1$-regularization approximation polynomial, respectively. Finally, we give numerical examples to illustrate these theoretical results and show that well-chosen regularization parameter can provide good performance approximation, with or without contaminated data.

报告人简介：

安聪沛, 本科、硕士毕业于中南大学，师从向淑晃，博士毕业于香港理工大学，师从Chen Xiaojun，Ian H Sloan，西南财经大学经济数学学院副教授、博导。曾在暨南大学数学系工作7年，广东省计算数学会常务理事兼副秘书长。主要从事点集分布理论以及计算方法应用研究，在球面t-设计，高震荡函数积分计算、插值理论和方法有较好的研究结果。主持国家自然科学基金二项，省部级自然基金一项，中央高校基金二项，在SIAM J. Numer.Anal., J.Comput.and Appl. Math., Appl.Math and Comput. 等计算数学期刊发表论文多篇。多次应邀访问香港理工大学，香港中文大学，香港大学，香港城市大学，中国科学院数学与系统科学研究院等著名学术机构。