特邀英国剑桥大学Prof. Arieh Iserles来我校做报告

发布单位:天际新闻网创建者:蔡惠华发布时间:2018-10-15浏览量:1308

报告题目:Skew-symmetric differentiation matrices and spectral methods on the real line

 

报告时间:2018年10月15日(周一)下午15: 20--16: 20

报告地点:尚贤楼706会议室

报告人:Prof. Arieh Iserles (剑桥大学)

主持人:蒋勇教授

 

专家简介:Arieh Iserles教授是国际著名数值分析学家、英国剑桥大学分析中心主任、应用数学和理论物理系终身教授。在微分方程的李群方法、高振荡积分的高效计算等方面做出了突出贡献。1999年获得挪威Lars Onsager奖,2012年获得英国伦敦数学学会授予的David Crighton奖,2012年应邀在第6届欧洲数学大会上作邀请报告。Arieh Iserles 教授现任或曾任国际著名期刊《Acta Numerica》、《Foundations of Computational Mathematics》、《IMA Journal of Numerical Analysis》的主编,以及国际著名计算数学期刊《Numerische Mathematic》、《Advances in Computational Mathematics》、《Calcolo》等的编辑。

 

报告内容摘要:A most welcome feature of orthogonal bases employed in spectral methods is that their differentiation matrix is skew symmetric, since this makes energy conservation automatic in conservative time-evolving problems. A familiar example is given by Hermite functions, which are dense in $L(-\infty,\infty)$ and give raise to a skew-symmetric, tridiagonal differentiation matrix.In this talk, describing joint work with Marcus Webb (KU Leuven), we present full characterisation of all orthogonal systems acting on $L2(-\infty,\infty)$, dense either there or in a Paley—Wiener space, and that have a differentiation matrix which is skew-symmetric, tridiagonal and irreducible. We also present a constructive algorithm for their generation — essentially, given any symmetric Borel measure on $(-\infty,\infty)$ or on $(-a,a)$ for some $a>0$, there exists a unique (up to rescaling) basis of this kind and it can be generated constructively. We conclude with a number of examples, related to Konoplev, Carlitz and Freud measures.Finally, we address the more general question of skew-Hermitian differentiation matrices. This brings us to very recent work on a variant of Malmquist—Takenaka basis, which appears to tick every desirable box: an orthonormal system dense in $L2(-\infty,\infty)$, with tridiagonal skew-Hermitian differentiation matrix and whose generalised Fourier coefficients can be computed with a single FFT.

数学与统计学院

2018年10月12日