报告人：安聪沛（暨南大学）

报告题目：Regularized Weighted Least Squares by Orthogonal Polynomials

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. It can be shown that they are extentions of Wang-Xiang formula for polynomial interpolation.We then study the approximation quality of $\ell_2-$regularization approximation polynomial and 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：安聪沛副教授本科、硕士毕业于中南大学，博士毕业于香港理工大学，现任暨南大学数学系副教授，硕士生导师，广东省计算数学会常务理事兼副秘书长。主要研究兴趣包括球面布点与球面t-设计、函数逼近等。主持国家自然科学基金二项，省部级自然基金一项，在SIAM Journal on Numerical Analysis等计算数学知名期刊发表论文多篇。

报告时间：2018年10月28日上午10：00- 11：00.

报告地点：科技楼南楼702