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发表时间:2021-01-25 阅读次数:890次
报告题目: How much faster does the best approximation converge than classical orthogonal projections?
报 告 人:王海永 教授
报告人所在单位:华中科技大学数学科学亚投彩票网站app
报告日期:2021-01-25 星期一
报告时间:10:00-11:00
报告地点:腾讯会议ID:196688549, 密码: 200433
  
报告摘要:
The best approximation, which was initiated by Chebyshev in 1853, is an elegant idea in the area of polynomial approximations and every textbook on approximation theory has a chapter to introduce it. From the point of view of polynomial approximations in the maximum norm, there is no doubt that the best approximation is better than any other polynomial approximations of the same degree. However, its implementation is a nonlinear problem and the cost is prohibitively expensive when the degree is large.
 
In this talk, we compare the convergence behavior of classical orthogonal projections, such as Legendre, Gegenbauer and Jacobi projections, and the best approximation. We show that the convergence rates of both Legendre and Chebyshev projections are almost the same as that of best approximations for analytic and differentiable functions. For Gegenbauer and Jacobi projections, however, their rates of convergence is the same as that of best approximations only under very restrictive conditions on the parameters of Gegenbauer and Jacobi polynomials. 

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