时间：2024年6月21日9：00—11：00

地点：腾讯会议 989 324 548

简历：余波，男，1979年生，三峡大学理学院数学系教授，硕士生导师。2006年中国科学院研究生院博士毕业。2008-2009纽约州立大学上州医科大学访问学者，2011-2012香港城市大学访问研究员，2012-2013及2016-2017纽约州立大学奥尔巴尼分校访问学者。主要研究方向是计算与应用调和分析及其应用。近年来在Applied Mathematical Modelling, IEEE Signal Processing Letters, Fractals等杂志上发表论文多篇，主持完成国家自然科学基金青年基金一项，教育部留学回国人员科研启动基金一项，中船重工第七一零研究所委托研究项目三项。

题目：Fast algorithms for computing the Hilbert transform of a given function with cubic splines

摘要：It is important to compute the Hilbert transform of a given function defined on a finite interval. In 2013, Micchelli and his collaborators proposed a fast algorithm, which is called the Hilbert spline transform, to calculate the Hilbert transform of a given function on a finite interval with computational complexity O(nlogn), where the spline knots were chosen to be the midpoints of sampling points. A natural question is that, whether or not, the spline knots can be chosen to be the same as the sampling points. This paper gives a positive answer to this question. Besides, the analytic expression of the Hilbert transform of B-splines of any order is also established. Furthermore, the problem of how to choose spline coefficients, using quasi-interpolation method or interpolation method, is also considered, although both makes sure an optimal approximation order. Several interesting numerical examples are implemented and compared with most of the existing methods. Numerical results show that the proposed algorithm has a relatively high computational accuracy as well as a relatively low computational complexity.