報告題目：An intermediate eigenvalue problem in electronic structure calculation
報 告 人：張紹良 教授 日本名古屋⼤學
報告時間：2022年9月13日 上午9:00-10:00
報告地點：騰訊會議 ID：722-811-073
會議鍊接：https://meeting.tencent.com/dm/qNV403RKKtel
校内聯系人：呂俊良 lvjl@jlu.edu.cn
報告摘要：We consider the generalized eigenvalue problem A x = λB x where A is a real symmetric matrix and B is a real symmetric positive definite matrix. A property of this problem is that all the eigenvalues are real, and it is often needed to compute a number of eigenvalues which are important for applications.In the field of electronic structure calculation, there has emerged a need to find the eigenvalues related to luminescence of organic materials. The targets are small in number,and from the atomic configuration of the material it is determined which eigenvalues need to be computed.In this talk, we present a bisection approach to obtaining the eigenvalues related to the luminescence.By iteratively searching and narrowing the interval within which the target eigenvalues exist,we can find them without computing unrelated eigenvalues.
報告人簡介：張紹良教授于吉林⼤學數學系計算算數學專業獲學士學位，于日本築波⼤學獲理⼯學碩⼠學位及⼯學博⼠學位，曾任職于日本名古屋⼤學⼯學部、日本築波⼤學電子情報⼯學系、日本東京⼤學⼯學系等。曾/現任⽇本應用數理學會理事, ⽇本應用數理學會理事會監事,East Asia SIAM的秘書,以及包括 International Journal of Numerical Analysis and Modeling，East Asian Journal on Applied Mathematics,Journal of Mathematical Research and Exposition, 及Journal of Information and Computational Science等雜志編委。張紹良教授在近年國際熱門研究課題“乘積型疊代法”⽅⾯，開拓了⼀個新的研究⽅向。在改良著名疊代法 Bi-CGSTAB的同時，根據 Lanczos 三階遞推公式，成功地建⽴了線性⽅程組求解的乘積疊代法的統⼀模型。由此統⼀模型，可簡單地推導出著名的 CGS法，Bi-CGSTAB法，Bi-CGSTAB2法，并可推導出新⽅法：GPBi-CG法。設計出的算法GPBi-CG法在理論上有獨特的見解，在實際問題的應⽤上可解上百萬線性形⽅程組。各種計算結果表明GPBi-CG法是國際上現有的疊代法中精度最⾼，疊代速度最快，計算效率最有效的算法之⼀。
