报告题目：An intermediate eigenvalue problem in electronic structure calculation

报 告 人：张绍良 教授 日本名古屋⼤学

报告时间：2022年9月13日 上午9:00-10:00

报告地点：腾讯会议 ID：722-811-073

会议链接：https://meeting.tencent.com/dm/qNV403RKKtel

校内联系人：吕俊良 lvjl@jlu.edu.cn

报告摘要：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.

报告人简介：张绍良教授于吉林⼤学数学系计算算数学专业获学士学位，于日本筑波⼤学获理⼯学硕⼠学位及⼯学博⼠学位，曾任职于日本名古屋⼤学⼯学部、日本筑波⼤学电子情报⼯学系、日本东京⼤学⼯学系等。曾/现任⽇本应用数理学会理事, ⽇本应用数理学会理事会监事,East Asia SIAM的秘书,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等杂志编委。张绍良教授在近年国际热门研究课题“乘积型迭代法”⽅⾯，开拓了⼀个新的研究⽅向。在改良著名迭代法 Bi-CGSTAB的同时，根据 Lanczos 三阶递推公式，成功地建⽴了线性⽅程组求解的乘积迭代法的统⼀模型。由此统⼀模型，可简单地推导出著名的 CGS法，Bi-CGSTAB法，Bi-CGSTAB2法，并可推导出新⽅法：GPBi-CG法。设计出的算法GPBi-CG法在理论上有独特的见解，在实际问题的应⽤上可解上百万线性形⽅程组。各种计算结果表明GPBi-CG法是国际上现有的迭代法中精度最⾼，迭代速度最快，计算效率最有效的算法之⼀。